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

Abstract

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.

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

“…The work on applications of chaotic synchronization in secure communication has grown dramatically in recent years [ 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 ]. Developing control systems for synchronization of various chaotic systems has been one of the main focuses of prior works, aiming to improve security in communication.…”

Special Characteristics and Synchronizations of Multi Hybrid-Order Chaotic Systems

“…It is known that the evolutions of chaotic systems sensitively rely on the special initial conditions and parameters, as two identical chaotic systems start from slightly different initial conditions or parameters can separate exponentially with time. It is the interesting features and its potential applications in image encryptions, pseudo random number generators and secure communications [ 2 , 3 , 4 , 5 , 6 ] that enable numerous researchers to devote in finding the new chaotic models, for instance, enhanced integer chaotic maps, hidden attractors [ 7 , 8 , 9 ] and integer conservative chaotic systems. Chen chaotic system is applied to produce random sequences.…”

“…The mentioned articles made some great innovations in generalization of chaotic systems and secure communications based on fractional chaos [ 2 ]. Compared with integer chaotic system, the fractional chaotic system with fractional order can regard the fractional order as another type of the secret key in the process of image, video encryptions and secure communications [ 22 , 23 , 24 ].…”

The Synchronization of N Cascade‐Coupled Chaotic Systems

“…Since Pecora and Carrol reported the discovery of synchronization for two chaotic systems by circuits implementation [1], the exciting phenomenon has gained much attention. In various elds, such as secure communication, signal processing, and life sciences, many types of chaotic synchronization are proving to be increasingly useful [2][3][4][5]. e design of novel synchronization models is necessary in such applications and thus motivating researchers to develop it, such as phase synchronization [6], projective synchronization [7], generalized synchronization [8], complex synchronization [9], modulus synchronization [10], and hybrid dislocated synchronization [11].…”