scholarly journals Secure Communication of Fractional Complex Chaotic Systems Based on Fractional Difference Function Synchronization

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jiaxun Liu ◽  
Zuoxun Wang ◽  
Minglei Shu ◽  
Fangfang Zhang ◽  
Sen Leng ◽  
...  
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Digital Signal ◽  
Fractional Difference ◽  
Voice Signal ◽  
Difference Function ◽  
Image Cryptosystem ◽  
Definition Of ◽  
Complex Chaotic Systems ◽  
Function Synchronization

Fractional complex chaotic systems have attracted great interest recently. However, most of scholars adopted integer real chaotic system and fractional real and integer complex chaotic systems to improve the security of communication. In this paper, the advantages of fractional complex chaotic synchronization (FCCS) in secure communication are firstly demonstrated. To begin with, we propose the definition of fractional difference function synchronization (FDFS) according to difference function synchronization (DFS) of integer complex chaotic systems. FDFS makes communication secure based on FCCS possible. Then we design corresponding controller and present a general communication scheme based on FDFS. Finally, we respectively accomplish simulations which transmit analog signal, digital signal, voice signal, and image signal. Especially for image signal, we give a novel image cryptosystem based on FDFS. The results demonstrate the superiority and good performances of FDFS in secure communication.

A SIMPLE WAY TO SYNCHRONIZE CHAOTIC SYSTEMS WITH APPLICATIONS TO SECURE COMMUNICATION SYSTEMS

1993 ◽  
Vol 03 (06) ◽  
pp. 1619-1627 ◽  
Author(s):  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Lyapunov Exponents ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Functional Form ◽  
Response System ◽  
Definition Of

In this paper, we provide a scheme for synthesizing synchronized circuits and systems. Synchronization of the drive and response system is proved trivially without the need for computing numerically the conditional Lyapunov exponents. We give a definition of the driving and response system having the same functional form, which is more general than the concept of homogeneous driving by Pecora & Carroll [1991]. Finally, we show how synchronization coupled with chaos can be used to implement secure communication systems. This is illustrated with examples of secure communication systems which are inherently error-free in contrast to the signal-masking schemes proposed in Cuomo & Oppenheim [1993a,b] and Kocarev et al. [1992].

scholarly journals A New Synchronization Method for Time-Delay Fractional Complex Chaotic System and Its Application

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3305
Author(s):  
Junmei Guo ◽  
Chunrui Ma ◽  
Xinheng Wang ◽  
Fangfang Zhang ◽  
Michaël Antonie van Wyk ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Time Delay ◽  
Secure Communication ◽  
Speech Communication ◽  
Lü System ◽  
Adomian Decomposition ◽  
Speech Transmission ◽  
Definition Of ◽  
Lu System ◽  
Function Synchronization

This paper proposes a class of time-delay fractional complex Lu¨ system and utilizes the adomian decomposition algorithm to study the dynamics of the system. Firstly, the time chaotic attractor, coexistence attractor and parameter space are studied. The bifurcation diagram and complexity are used to analyze the dynamic characteristics of the system. Secondly, the definition of modified fractional projective difference function synchronization (MFPDFS) is introduced. The corresponding synchronous controller is designed to realize the MFPDFS of the time-delay fractional complex Lu¨ system. Thirdly, based on the background of wireless speech communication system (WSCs), the MFPDFS controller is used to realize the secure speech transmission. Finally, the effectiveness of the controller is verified by numerical simulation. The signal-noise ratio (SNR) analysis of speech transmission is given. The performance of secure communication is verified by numerical simulation.

scholarly journals Enhanced Symplectic Synchronization between Two Different Complex Chaotic Systems with Uncertain Parameters

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Cheng-Hsiung Yang
Keyword(s):  
Numerical Simulations ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Asymptotical Stability ◽  
Sufficient Condition ◽  
Uncertain Parameters ◽  
Null Solution ◽  
Special Cases ◽  
Error Dynamics ◽  
Complex Chaotic Systems

An enhanced symplectic synchronization of complex chaotic systems with uncertain parameters is studied. The traditional chaos synchronizations are special cases of the enhanced symplectic synchronization. A sufficient condition is given for the asymptotical stability of the null solution of error dynamics. The enhanced symplectic synchronization may be applied to the design of secure communication. Finally, numerical simulations results are performed to verify and illustrate the analytical results.

A Robust Secondary Secure Communication Scheme Based on Synchronization of Spatiotemporal Chaotic Systems

2013 ◽  
Vol 68 (8-9) ◽  
pp. 573-580 ◽  
Author(s):  
Xing-Yuan Wang ◽  
Hao Zhang
Keyword(s):  
Communication System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Digital Signal ◽  
Stable Theory ◽  
Asymptotic Convergence ◽  
Hyperchaotic System ◽  
Communication Scheme ◽  
Chaotic Secure Communication ◽  
Spatiotemporal Chaotic System

This paper deals with the synchronization of spatiotemporal chaotic systems and presents a new robust secondary chaotic secure communication system for digital signal transmissions which can recover digital signal even though the transmitted signal is influenced by limited noise. The transmitter terminal and the receiver terminal both contain a spatiotemporal chaotic system and a hyperchaotic system. The asymptotic convergence of the errors between the states of the transmitter terminal and the receiver terminal has been proved based on the Lyapunov stable theory and active-passive decomposition (APD) method. Moreover, a random digital signal and a binary Lena image are encrypted and decrypted successfully to verify the efficiency of the proposed robust secure communication system.

Finite Time Synchronization of Chaotic Systems Without Linear Term and Its Application in Secure Communication

2021 ◽  
Vol 15 (4) ◽  
pp. 54-78
Author(s):  
Shuru Liu ◽  
Zhanlei Shang ◽  
Junwei Lei
Keyword(s):  
Finite Time ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Difficult Problem ◽  
Stable System ◽  
Convergence Time ◽  
Unknown Parameters ◽  
Communication Scheme ◽  
Definition Of

A definition of finite time synchronization of chaotic system was proposed, and a special theorem was proposed to solve the difficult problem of constructing a finite time stable system. After that, a hybrid construction method was proposed by integrating a common stable system and a finite time stable system. That reveals how to construct a finite time stable system, and it is very useful in secure communication since the convergence time is a very important factor that will affect its application in engineering realization. Above theorem and method was applied in the chaotic synchronization and two kinds of synchronization methods were proposed with estimation of unknown parameters. At last, a secure communication scheme was constructed by using above finite time synchronous method of chaotic systems. Also, numerical simulation was done, and the rightness of all the above proposed theorems and methods was shown.

Hybrid Delayed Synchronizations of Complex Chaotic Systems in Modulus-Phase Spaces and Its Application

2015 ◽  
Vol 11 (4) ◽  
Author(s):  
Luo Chao
Keyword(s):  
Secure Communication ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Complete Synchronization ◽  
Modified Projective Synchronization ◽  
Synchronization Scheme ◽  
Complex Chaotic Systems ◽  
Real Number Field

Compared with chaotic systems over the real number field, complex chaotic dynamics have some unique properties. In this paper, a kind of novel hybrid synchronizations of complex chaotic systems is discussed analytically and numerically. Between two nonidentical complex chaotic systems, modified projective synchronization (MPS) in the modulus space and complete synchronization in the phase space are simultaneously achieved by means of active control. Based on the Lyapunov stability theory, a controller is developed, in which time delay as an important consideration is involved. Furthermore, a switch-modulated digital secure communication system based on the proposed synchronization scheme is carried out. Different from the previous works, only one set of drive-response chaotic systems can implement switch-modulated secure communication, which could simplify the complexity of design. Furthermore, the latency of a signal transmitted between transmitter and receiver is simulated by channel delay. The corresponding numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

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