Chaotic Masking Method Research Articles

Parametric fractional-order analysis of Arneodo chaotic system and microcontroller-based secure communication implementation

Chaotic systems are often used in cryptology applications thanks to their complex dynamic structures. By increasing the dynamic diversity of chaotic systems through fractional-order analysis, more complex systems for data security can be obtained. In this study, fractional calculus analyses of the Arneodo chaotic jerk system with cubic nonlinearity and its microcontroller-based chaotic masking application are presented. Numerical analyses such as bifurcation diagrams, spectral entropy complexity, and Lyapunov spectra are performed to examine the dynamic characteristics of the fractional-order system. The parametric analysis indicates the presence of chaotic states in the system for nearly all fractional-order values ranging from 0.55 to 1. In this manner, the study focuses on investigating the minimum applicable fractional-order value for use in secure communication applications, constituting the main contribution of this research. Consequently, the dynamic diversity and unpredictability of the cubic system are greatly increased. Moreover, two fractional-order Arneodo chaotic (FOAC) systems with distinct initial conditions are synchronized using a single-state fractional-order sliding mode controller (FOSMC). Finally, an innovative secure communication system based on a microcontroller is designed and implemented by employing the chaotic masking method. As anticipated, the voltage outputs of the microcontroller-based secure communication application demonstrated good agreement with the numerical simulations.

Optical cryptographic communications with non-identical chaotic laser systems

"We report secure data transmission performed using chaotic lasers with different external cavity geometries and applying the chaotic masking method based on subcarrier and phase modulations of the chaotic optical carrier. Two semiconductor lasers with similar multimode emission spectra and self-optical feedback provided, respectively, by ring and linear external cavities, were optically coupled and chaotically synchronized into a master – slave scheme. The transmitted message frequency modulates the radio frequency signal which modulates in phase the master chaotic carrier. Based on the robustness of the used encryption method and the synchronization characteristics of the two lasers, the decryption is conducted by the simple radio frequency spectrum monitoring of the slave emission."

A novel five-term 3D chaotic system with cubic nonlinearity and its microcontroller-based secure communication implementation

Data security has gained importance over the years. Thus, cryptology is becoming a more popular phenomenon. In cryptology applications, a chaotic system with third- or higher-order terms is more difficult to decrypt. The main advantages of a system with fewer terms are easier to implement and cost-effective. Therefore, the motivation of this study is to introduce a new five-term 3D chaotic flow having cubic nonlinearity, a linear term, a constant term, and two other nonlinear terms. Despite the five-term hidden attractor with cubic nonlinearity in the literature, the proposed system has four equilibria, so it is a self-excited attractor. To examine the dynamical characteristic of the introduced system, we performed numerical analyses, such as time series, phase plains, equilibria, multistability, bifurcation, and Lyapunov spectra. Furthermore, the response and drive systems with different initial conditions obtained from the system were established, and their synchronization using only one control signal was applied. To prove the applicability of proposed system, its circuit implementation was realized by utilizing commercially available devices. An inventive microcontroller-based secure communication using the chaotic masking method was also designed and implemented. As expected, the demonstrated experimental results were in good agreement with the numerical analyses.

A four-scroll chaotic generator based on two nonlinear functions and its telecommunications cryptography application

This paper describes a new chaotic jerk system based on two different nonlinear functions. The modified signum and rectangular functions are incorporated into the system at different positions. The system can generate double-scroll and new four-scroll chaotic attractors by adjusting only one coefficient (k). The chaotic behaviors of the proposed system are investigated by the Lyapunov spectrum and period distribution of state variable × of the bifurcations. The complexity of the proposed chaotic system is computed by the Kaplan-Yorke dimension of 2.30. The coexisting attractors and basin of attraction are also included to verify the system's dynamic to the initial conditions. The PCB prototype's commercially available OPAMP and passive components are realized to confirm the numerical studies. The experimental results and the numerical results are agreeable in signals and attractors. The chaotic masking method is applied for encrypting the data for secure communication. The efficient encrypted signal can be obtained, and the decrypted data can be correctly received after successful synchronization.

Multi-State Synchronization of Chaotic Systems with Distributed Fractional Order Derivatives and Its Application in Secure Communications

This study investigates multiple synchronizations of distributed fractional-order chaotic systems. These systems consider unknown parameters, disturbance, and time delays. A robust adaptive control method is designed for multistage distributed fractional-order chaotic systems. In this paper, system parameters are changed step by step. Using Lyapunov’s function, while the synchronization error convergence to zero is guaranteed, adaptive rules are designed to estimate the parameters. Then, a secure communication scheme is proposed using the new chaotic masking method. Finally, the simulations are performed on a chaotic system of distributed Duffing fractional order. The results show the high efficiency of the proposed synchronization scheme using robust adaptive control, despite the parametric uncertainties, external disturbance, and variable and unknown time delays. Then, the simulations were performed on the sinusoidal signals of the message in the application of secure communications. The results showed the success of the proposed masking scheme with synchronization in coding and decoding information.

Internet of Medical Things Application in Encryption of Medical Images Based on Synchronization of Multi-state Chaotic Systems

Introduction: Studies on the security and interoperability of Internet of medical things (IoMT)in health are still scarce. The most important effects of the IoMT on health care are the ability to exchange information and reduce hospitalization and health care costs. The main challenges of the IoMT in healthcare are security and protection of privacy, among which encryption of images is very important in the field of communication and security. The main purpose of this study was to design a secure channel for encrypting and sending medical data. Methods: This study presents a new method for encrypting medical images to preserve patient information by synchronizing two chaotic systems. The use of chaotic signals as carriers of medical images greatly enhances security and greatly reduces the possibility of detection. The idea of synchronization of chaotic systems was presented in multi states with fixed time delay. In this idea, with the help of Lyapunov’s theory of stability, a controller was designed to establish the stability of the closed-loop system. Then, according to the synchronization idea and its error, a chaotic masking method was proposed to encrypt patient images. The simulation and accuracy of the results of the presented method were investigated in MATLAB software version 2020.Results: The simulations were performed on medical color images and CT, MRI, and X-ray images. Encrypted and recovered images were obtained by the proposed system. To evaluate the performance of the proposed method, various criteria including image histogram, signal-to-noise rate, correlation, and entropy of information were evaluated. The results showed the excellent image encrypting efficiency of the proposed method.Conclusion: Using the proposed method, medical images were encrypted based on a secure protocol, and then with satisfactory quality, images were recovered after transmission.

A new synchronisation method of fractional-order chaotic systems with distinct orders and dimensions and its application in secure communication

In this paper, an adaptive generalised function projective synchronisation scheme of fractional-order chaotic systems with different dimensions and orders and fully unknown parameters is presented. On the basis of the Lyapunov method of fractional-order systems, a stability theorem of the fractional-order system with non-identical orders is proven. Using the fractional-order controller and adaptive control theory, sufficient conditions for synchronisation and unknown parameters update rules are obtained. Theoretical analysis and numerical simulations are provided to verify the validity of the proposed scheme. Moreover, synchronisation results are applied to secure communication via modified chaotic masking (MCM) method. The unpredictability of the scaling function matrix and the use of fractional-order systems with different orders can increase the security of the cryptosystem. The security analysis shows that the introduced algorithm has large key space, high sensitivity to encryption keys, higher security and the acceptable encryption speed.

Design of Adaptive-Robust Controller for Multi-State Synchronization of Chaotic Systems with Unknown and Time-Varying Delays and Its Application in Secure Communication.

In this paper, the multi-state synchronization of chaotic systems with non-identical, unknown, and time-varying delay in the presence of external perturbations and parametric uncertainties was studied. The presence of unknown delays, unknown bounds of disturbance and uncertainty, as well as changes in system parameters complicate the determination of control function and synchronization. During a synchronization scheme using a robust-adaptive control procedure with the help of the Lyapunov stability theorem, the errors converged to zero, and the updating rules were set to estimate the system parameters and delays. To investigate the performance of the proposed design, simulations have been carried out on two Chen hyper-chaotic systems as the slave and one Chua hyper-chaotic system as the master. Our results showed that the proposed controller outperformed the state-of-the-art techniques in terms of convergence speed of synchronization, parameter estimation, and delay estimation processes. The parameters and time delays were achieved with appropriate approximation. Finally, secure communication was realized with a chaotic masking method, and our results revealed the effectiveness of the proposed method in secure telecommunications.

A new approach for security of wireless sensor networks based on anti-synchronization of the fractional-order hyper-chaotic system

Chaotic systems have wide applications in secure communication engineering and cryptography. In this paper, improved nonlinear predictive control with whale algorithm for anti-synchronization of a fractional-order economic hyper-chaotic system is used for increasing the security of wireless sensor networks and preventing intrusion. By chaotic masking method and the T-S fuzzy model, the message signal is encoded at the wireless sensor side and it is placed along the transmitter route. In the central station, the message signal is decoded using the T-S fuzzy model and the predictive control by anti-synchronizing the fractional-order hyper-chaotic slave system. To reduce the effect of disturbances, a sign function of error is added to the predictive control. Finally, simulation results indicate the proper performance of the proposed nonlinear predictive control for anti-synchronizing the fractional-order hyper-chaotic systems in secure communications.

Combination Projective Synchronization in Fractional-Order Chaotic System with Disturbance and Uncertainty

In this manuscript, we study combination projective synchronization (CPS). In CPS, matrix projective combination synchronization (MPCS) and inverse matrix projective combination synchronization (IMPCS) between non-identical fractional-order complex chaotic systems subjected to uncertainty and external disturbance is investigated. Matrix projective synchronization (MPS) and inverse matrix projective synchronization is obtained when the scaling factor is a constant matrix, which gives the assurance of high security in secure communication and image encryption. Based on the Lyapunov stability theory and appropriate active control technique, the MPCS and IMPCS between two master systems and one slave system has been achieved. Based on the MPCS synchronization, a scheme of secure communication is presented, and the message signals are transmitted using the chaotic signal masking method. Finally, numerical simulations have been provided, which shows that our theoretical results are in complete agreement will the graphical one.

Synchronization for Incommensurate Riemann–Liouville Fractional-Order Time-Delayed Competitive Neural Networks With Different Time Scales and Known or Unknown Parameters1

Synchronization for incommensurate Riemann–Liouville fractional competitive neural networks (CNN) with different time scales is investigated in this paper. Time delays and unknown parameters are concerned in the model, which is more practical. Two simple and effective controllers are proposed, respectively, such that synchronization between the salve system and the master system with known or unknown parameters can be achieved. The methods are more general and less conservative which can also be applied to commensurate integer-order systems and commensurate fractional systems. Furthermore, two numerical ensamples are provided to show the feasibility of the approach. Based on the chaotic masking method, the example of chaos synchronization application for secure communication is provided.

Adaptive synchronisation of memristor-based neural networks with leakage delays and applications in chaotic masking secure communication

ABSTRACTChaotic synchronisation has caused extensive attention due to its potential application in secure communication. This paper is concerned with the problem of adaptive synchronisation for two different kinds of memristor-based neural networks with time delays in leakage terms. By applying set-valued maps and differential inclusions theories, synchronisation criteria are obtained via linear matrix inequalities technique, which guarantee drive system being synchronised with response system under adaptive control laws. Finally, a numerical example is given to illustrate the feasibility of our theoretical results, and two schemes for secure communication are introduced based on chaotic masking method.

Design of a switched hyperchaotic system and its application

This paper proposes an automatically switched hyperchaotic system between two different hyperchaotic systems. One is designed by changing three equations of another system. Two linear-term parameters and one nonlinear term are changed for corresponding equations, and characteristics have been analysed in details. There are two main contributions of this paper. One is that the new system automatically switches. Another is that the other hyperchaotic system is constructed by changing more parameters compared to the existing switched chaotic systems. Furthermore, the dynamical characteristics about the attractor of the new switched hyperchaotic system are simulated by Matlab. Correspondingly, multisim simulations are also conducted. All these results are consistent with each other and verify the existence of the attractor of the new system. The system is also used for a secure communication implementation based on chaotic masking method. The simulation for secure communication application is conducted and shows the success of this application.

Secure Communication with Chaos and Electronic Circuit Design Using Passivity-Based Synchronization

This work deals with the passive control-based chaos synchronization with circuit design for secure communication. First, the numerical simulation and electronic circuit design of a simple five-term chaotic system are performed. The numerical simulation and electronic circuit design outputs have confirmed each other. Then, the passive control method is applied for synchronizing two identical five-term chaotic systems using only one state control signal. After the synchronization study, design and analysis for secure communication by chaotic masking method are conducted in Matlab–Simulink platform. Finally, an electronic circuit design is performed for the designed communication system. In the designed communication system with Matlab–Simulink platform and electronic circuit design, information signal which is sent from the transmitter unit is successfully retrieved at the receiver unit. As a result, the electronic circuit design has shown that a single state passivity-based synchronization signal can be effectively used for secure data communication applications for the real environment.

Chaotic system synchronization of state-observer-based fractional-order time-delay

A lot of studies of control highlight fractional calculus in modeling systems and designing controllers have been carried out. More recently, a lot of chaotic behaviors have been found in fractional-order systems. Then, controlling the fractional-order systems, especially controlling nonlinear fractional-order systems has become a hot research subject. The design of state estimators is one of the essential points in control theory. Time delays are often considered as the sources of complex behaviors in dynamical systems. A lot progress has been made in the research of time delay systems with real variables. In recent years, fractional-order time-delay chaotic synchronization and chaotic secure communication have received ever-increasing attention. In this paper we focus our study on the synchronization of fractional-order time-delay chaotic systems and its application in secure communication. Firstly, based on the Lipschitz condition, the nonlinear fractional-order time-delay system is proposed. Secondly, the fractional-order time-delay observer for the system is constructed. The necessary and sufficient conditions for the existence of the fractional-order observer are given by some lemmas. Thirdly, the synchronous controller is designed based on the state observer and the stability theory of fractional-order system. Instead of the state variables, the output variables of drive system and response system are used to design the synchronous controller, which makes the design much more simple and practical. With the Lyapunov stability theory and fractional order matrix inequalities, the method of how to obtain the parameters of the controller is presented. The sufficient conditions for asymptotical stability of the state error dynamical system are derived. After that, with the Chen fractional-order time-delay chaotic system, the synchronous controller is designed to make the system run synchronously. Finally, the proposed approach is then applied to secure communications, where the information signal is injected into the transmitter and simultaneously transmitted to the receiver. With the observer design technique, a chaotic receiver is then derived to recover the information signal at the receiving end of the communication. In the conventional chaotic masking method, the receiver is driven by the sum of the information signal and the output of the transmitter, whose dynamics is autonomous. The simulation results show that the design of the synchronous controller works effectively and efficiently, which implies that the proposed fractional order time-delay observer in this paper runs effectively. The proposed method is able to be applied to other fractional order time-delay chaos systems, and also to chaotic secure communication system.

A new 3D chaotic system: Dynamical analysis, electronic circuit design, active control synchronization and chaotic masking communication application

This study presents a new three dimensional continuous time chaotic system. Dynamical analysis and numerical simulation of the new chaotic system were first carried out. Then electronic circuit design of the new chaotic system was implemented considering practical applications. The numerical and electronic circuit simulation results were found to be in good accordance. Besides, synchronization by active control was realized for secure communication applications, followed by designing a communication system with chaotic masking method. Finally, a secure signal masking application was implemented on Matlab platform. In the developed secure communication system, information signal sent over noisy channel was successfully retrieved at the receiver.

一个新五维超混沌电路及其在保密通讯中应用

超混沌系统比普通混沌系统的动态行为更加难以预测，因此在保密通讯中具有更重要的应用价值。本文在Chen混沌系统中引入两个状态变量和一个反向控制器构造了一个新的五维超混沌系统。首先讨论了新系统的定点稳定性及其相空间动力学行为，发现新系统有3个正的Lyapunov指数。设计了该系统的模块化电路，示波器观测结果与数值模拟结果一致。其次采用驱动响应式同步方式实现了新系统的混沌同步，并数值模拟了方波信号的混沌保密通讯过程，利用混沌掩盖法完成了新系统方波信号的混沌保密通讯电路。最后，分别采用混沌信号加入到图片中和图片数字化加入到混沌信号中两种不同的方式实现图片的混沌保密通讯过程。对比研究表明后者的加密效果更好，具有更高的信息还原度。 The dynamic behavior of a hyper-chaotic system is much more difficult to be predicted than that of a normal chaos system. Therefore, it becomes very useful in the secure communication. This paper constructed a new five dimensional hyper-chaotic circuit based on Chen system when the two state variables and an inverse controller are introduced. First, the stability of the fixed points and dynamic behavior of the phase space of the new system are discussed, and three positive Lyapunov exponents are found. Modular circuit of the system is designed. The results of circuit simulation are in agreement with the numerical simulation. Then chaos synchronism of the system is achieved with drive-response synchronization method. Numerical simulation of the secure communication process for the square wave signal is given, and chaotic masking method is used to realize the secure communication circuit with square wave voltage signal of the system. Finally, two ways to deal with secure communication are discussed; one is the chaotic signal mixed with the image, and the other is chaotic signal added to the digital image. It is shown that the latter is better than the former in the effect on secure communication, and is more suitable for information reversion.

Effects of spontaneous emission noise in semiconductor lasers on chaotic optical communication systems

A chaotic optical communication system based on external optical feedback is constructed. By introducing the Langevin noise sources, the master-slave rate equations including spontaneous emission noise characteristics are deduced. Utilizing the obtained mathematical model, two kinds of possible chaos synchronization in the system, i.e. complete chaos synchronization and generalized mode-locking chaos synchronization, are studied. The effects of the spontaneous emission noises of the two lasers on the two types of synchronization as well as the chaotic outputs of the transmitter and receiver are discucsed. Finally, for a sequence of pseudorandom digital bits at 2.5Gb/s bit rate, the encoding/decoding process basing on chaotic masking method is presented, and the effects of noise on decoding performance are examined.

Chaotic wavelength division multiplexing for optical communication

We demonstrate wavelength division multiplexing with chaotic subcarriers in two pairs of one-way-coupled Nd:YVO4 microchip lasers. Two individual digital messages are encoded on two chaotic carriers with different wavelengths in two transmitters by the chaotic masking method, and the mixed signals are sent to two receivers. Dual synchronization of chaos is used to obtain the original chaotic waveforms in the receivers. Two messages are decoded by filtering the difference of the laser outputs between the transmitter and the receiver by use of a low-pass filter for each pair of lasers. The message recovery can be achieved more easily when messages with small amplitude and low frequency are used.