Abstract
In this paper, we put forward on the drive-response synchronization in shape for four-dimensional (4-D) continuous chaotic system, using the basic theory of plane curves in classical differential geometry. For 4-D continuous system, shape synchronization means the six-response systems have the same shape of chaotic attractor as the six projective systems of driver system. Numerical simulations are given to verify the theoretical analysis, which clearly shows that the shape controllers can really make two systems achieve shape synchronization in a quite short time. Moreover, a shape synchronization encryption algorithm for color image is proposed. Simulation results reveal the superiority of the proposed approach.
Highlights
With the development of computer, communication, and network technologies, information security issues have attracted more and more attention and become a current research hotspot [1]–[6]. Chaos has characteristics such as unpredictability, pseudo-randomness, and extreme sensitivity to initial value [7], [8], it has been widely used in complex networks [9]–[13], memristors [14]–[19], random number generators [20], [21], secrecy communication technologies [22]–[25], especially the image encryption [26]–[29]
Zhou et al proposed [30] a framework for parallel image encryption based on discretized chaotic map
In our previous work [71], [72], we proposed shape synchronization for a class of two-dimensional and three-dimensional chaotic systems and their application in secure communication system
Summary
With the development of computer, communication, and network technologies, information security issues have attracted more and more attention and become a current research hotspot [1]–[6]. If we pay attention to the shape of the drive chaotic attractor and control scheme, a new problem for drive-response synchronization may be proposed. (2) By getting the purpose of control, the group of shape controllers are designed based on the classical differential geometry technique Under these controllers, the chaotic attractor of response system and drive system have the same arc length measure and relative curvature,and two systems achieve shape synchronization in a short time. The shape controller is used to synchronize the response system in shape, decrypted the inverse operation of the encryption algorithm to obtain the decrypted image file During this period, the scheme used the shape characteristics variables of drive system as the driving signals.
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