Original research articleA memristor-based chaotic system and its application in image encryption
Introduction
As a branch of nonlinear science, chaos has large applied values in chaos synchronization [1], [2], secure communication [3], [4], image encryption [5], [6], [7] and so on. Recently memristor received a lot of attention from scholars in chaos field for memritor model can be used to construct the systems with complicated chaotic dynamical behavior.
Up to now, a number of memristive chaotic systems have been presented [8], [9], [10], [15]. For instance, Ref. [11] discussed a fractional order delayed memristor-based chaotic circuit system. Ref. [12] studied a memristor-based Shinriki’s circuit with multiple attractors. Ref. [13] investigated a memristor-based chaotic system with heart-shaped attractors and its implementation. Ref. [14] addressed the sliding-mode control problem on Chua’s memristive system with nonlinearity input. However most of memristive chaotic systems are based on classic memristor models. This is no good for information encryption because corresponding information decryption will be easy to achieve for hackers based on the prior information of classic chaotic systems.
With above concerns, a new chaotic system based on a memristor model which is different with classic memristor model will be presented in Section 2, Numerical simulation will be conducted to show the dynamical behavior of the new memristive chaotic system. Encryption method based on the new memristive chaotic system will be given to achieve image encryption in Section 3. Corresponding analysis will be made to demonstrate the effectiveness of our results. Finally the paper will be concluded in Section 4.
Section snippets
Main results
First, a new memristive chaotic system model is presented as followwhere M(w) is the memristor model such that
Let α = 0.5, b = 0.5, κ = 0.3, δ = 1, A = − 0.4, B = 1.65, C = − 1.5, D = 3, m = 1, n = 1.56, then corresponding numerical simulation results are shown in Fig. 1, Fig. 2.
Fig. 1 shows the phase diagram of the new memristive chaotic system. It can be seen that there exists a chaotic attractor in the
Image encryption
Based on the new memristive chaotic system and sampling time 0.001s, one can get chaotic sequences X(n), Y(n), Z(n).
Define variables
Let i = mod {n, 3}, and define the encryption chaotic sequence
Letwhere
We can get chaotic matrix .
For image IM×N, the encryption operation is defined as
Conclusion
In this paper, the problem on a memristive chaotic system and its application in image encryption has been discussed. A new memristive chaotic system has been presented, corresponding dynamical behavior has been analyzed. Then the encryption method based on the new memristive chaotic system has been given to achieve the image encryption. Finally encrypted image analysis have been made to demonstrate the effectiveness of the image encryption method.
Acknowledgments
This work was partially supported by the Project of Education Department of Sichuan Province (61134001), the Chunhui Plan Project of Ministry of Education (Z2015114), the National Natural Science Foundation of China (11626093), the Graduate Innovation Fund (ycjj2017171), the National Natural Science Foundation of China (NSFC:11626093) and the Natural Science Foundation of Hubei Provinces of China (2016CFB211).
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