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.

Generalized Hybrid Dislocated Function Projective Synchronization of Chaotic Systems with Time Delay

2014 ◽  
Vol 574 ◽  
pp. 672-678 ◽  
Author(s):  
Rui Li ◽  
Guang Jun Zhang ◽  
Tao Zhu ◽  
Xu Jing Wang ◽  
Jun Dong
Keyword(s):  
Time Delay ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Feedback Gain ◽  
Uncertain Parameters ◽  
Function Projective Synchronization ◽  
Feedback Control Method

In order to improve the security of secure communication, a novel generalized hybrid dislocated function projective synchronization (GHDFPS) was proposed and GHDFPS of time delay chaotic systems with uncertain parameters were researched in this paper. Due to time delay, the chaotic system can produce multiple positive Lyapunov exponential; this characteristic can enhance security in secure communications noticeably. Based on Lyapunove stability theory and modified hybrid feedback control method, the modified hybrid feedback controller and the parameter updating laws were designed for the GHDFPS between the two time delay chaotic systems with uncertain parameters. The feedback gain can be adjusted automatically according to the synchronization error values. Under the controller, generalized hybrid dislocated function projective synchronization of the two chaotic systems is achieved, and the uncertain parameters of response systems are identified. The chaotic item is added in the function scale factor. The chaotic item in the function scaling factor makes function scaling factor more complex and unpredictable. So this can enhance the features of indeterminism in secure communication. The time delay feedback Lorenz system as an example; by numerical simulations the effectiveness of the proposed method is demonstrated.

‎S‎ynchronization ‎of‎ different ‎dimensions‎ ‎fractional-‎order chaotic ‎systems with uncertain‎‎ ‎ parameters ‎and ‎secure ‎communication‎‎‎‎‎

2021 ◽  
Vol 39 (5) ◽  
pp. 57-72
Author(s):  
Vajiheh Vafaei ◽  
Hossein Kheiri ◽  
Aliasghar Jodayree Akbarfam
Keyword(s):  
Fractional Order ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Security Analysis ◽  
High Sensitivity ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Fractional Order Controller

In ‎this ‎paper, ‎an‎ adaptive ‎modified‎ function projective synchronization (‎AM‎FPS) ‎scheme‎ ‎of ‎different ‎dimensions‎‎ ‎fractional-‎order ‎chaotic systems with ‎fully ‎unknown parameters is ‎presented‎. ‎On the basis of ‎fractional‎ Lyapunov stability ‎theory ‎and adaptive control law‎,‎ a‎ ‎new‎ fractional-order controller ‎and‎ suitable ‎‎‎‎update ‎rules‎ for unknown parameters are ‎designed‎‎ to realize the ‎AMFPS‎ of different ‎fractional-‎order chaotic systems with ‎non-‎identical ‎orders ‎and different dimensions‎‎. ‎‎Theoretical analysis and numerical simulations are given to verify the validity ‎of ‎the proposed ‎method. ‎Additionally, ‎‎‎‎synchronization results ‎are applied to secure communication via ‎‎ ‎modified ‎‎‎‎masking ‎method. Due to the unpredictability of the scale ‎function ‎matrix‎ and ‎using‎ of ‎fractional-‎order ‎systems with different ‎dimensions ‎and ‎u‎nequal‎ ‎orders,‎‎ the proposed scheme has higher ‎security‎‎. The security analysis ‎‎‎demonstrate that the proposed algorithm ‎has ‎a large key space ‎and‎ high sensitivity to encryption keys ‎and it is ‎‎re‎sistance to all kind of ‎‎attacks‎.

Adaptive Complex Function Projective Synchronization of Uncertain Complex Chaotic Systems

2015 ◽  
Vol 11 (1) ◽  
Author(s):  
Fangfang Zhang ◽  
Shutang Liu
Keyword(s):  
Real World ◽  
Chaotic Systems ◽  
Complex Function ◽  
Projective Synchronization ◽  
Real Field ◽  
Complex Field ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Complex Chaotic Systems ◽  
Speed Gradient

Complex function projective synchronization (CFPS) is the most general synchronization and it enhances the security of communication. However, there always exist unknown parameters for chaotic systems in the real world. Considering all possible cases of unknown parameters of two complex chaotic systems, we design adaptive CFPS schemes and parameters update laws based on speed-gradient (SG) method. The convergence factors and pseudogradient condition are added to regulate the convergence speed and increase robustness. SG method is extended from real field to complex field. Numerical simulations are performed to demonstrate the effectiveness and feasibility of the proposed schemes.

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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