Memristor-based hyper-chaotic circuit for image encryption

doi:10.1088/1674-1056/abbbfe

中国物理B ›› 2020, Vol. 29 ›› Issue (11): 110504-.doi: 10.1088/1674-1056/abbbfe

Jiao-Jiao Chen(陈娇娇)¹^,², Deng-Wei Yan(闫登卫)¹^,², Shu-Kai Duan(段书凯)¹^,²^,³^,⁴^,⁵^,⁶, Li-Dan Wang(王丽丹)¹^,²^,³^,⁴^,⁵^,†()

收稿日期:2020-04-30 修回日期:2020-09-04 接受日期:2020-09-28 出版日期:2020-11-05 发布日期:2020-11-03

Memristor-based hyper-chaotic circuit for image encryption

Jiao-Jiao Chen(陈娇娇)^1,2, Deng-Wei Yan(闫登卫)^1,2, Shu-Kai Duan(段书凯)^1,2,3,4,5,6, and Li-Dan Wang(王丽丹)^{1,2,3,4,5, †}

1 College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China
2 Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Southwest University, Chongqing 400715, China
3 Intelligent Transmission and Control Technology Joint Engineering Laboratory, Chongqing 400715, China
4 Brain-inspired Computing and Intelligent Control Chongqing Key Laboratory, Chongqing 400715, China
5 Chongqing Collaborative Innovation Center for Brain Science, Chongqing 400715, China
6 School of Artificial Intelligence, Southwest University, Chongqing 400715, China

Received:2020-04-30 Revised:2020-09-04 Accepted:2020-09-28 Online:2020-11-05 Published:2020-11-03
Contact: ^†Corresponding author. E-mail: ldwang@swu.edu.cn
Supported by:
the National Key Research and Development Program of China (Grant No. 2018YFB1306600), the National Natural Science Foundation of China (Grant Nos. 62076207 and 62076208), and the Fundamental Science and Advanced Technology Research Foundation of Chongqing, China (Grant Nos. cstc2017jcyjBX0050).

摘要/Abstract

Abstract:

The memristor is a kind of non-linear element with memory function, which can be applied to chaotic systems to increase signal randomness and complexity. In this paper, a new four-dimensional hyper-chaotic system is designed based on a flux controlled memristor model, which can generate complex chaotic attractors. The basic dynamic theory analysis and numerical simulations of the system, such as the stability of equilibrium points, the Lyapunov exponents and dimension, Poincare maps, the power spectrum, and the waveform graph prove that it has rich dynamic behaviors. Then, the circuit implementation of this system is established. The consistency of simulation program with integrated circuit emphasis (SPICE) simulation and numerical analysis proves the ability to generate chaos. Finally, a new image encryption scheme is designed by using the memristor-based hyper-chaotic system proposed in this paper. The scheme involves a total of two encryptions. By using different security analysis factors, the proposed algorithm is compared with other image encryption schemes, including correlation analysis, information entropy, etc. The results show that the proposed image encryption scheme has a large key space and presents a better encryption effect.

Key words: memristor, SPICE simulation, hyper-chaotic system, image encryption

Jiao-Jiao Chen(陈娇娇), Deng-Wei Yan(闫登卫), Shu-Kai Duan(段书凯), Li-Dan Wang(王丽丹). [J]. 中国物理B, 2020, 29(11): 110504-.

Jiao-Jiao Chen(陈娇娇), Deng-Wei Yan(闫登卫), Shu-Kai Duan(段书凯), and Li-Dan Wang(王丽丹). Memristor-based hyper-chaotic circuit for image encryption[J]. Chin. Phys. B, 2020, 29(11): 110504-.

	x	y	z	w
S₁	−155885327979.4965	−519616.0680	5.1961	−300000.9767
S₂	155885376219.5367	519616.1484	−5.1961	−300001.0232
S₃	0	0	0	0

	x	y	z	w
S₄	−5.9999× 10⁻³⁸	−2.0020× 10⁻³⁸	−5.999× 10⁻³⁸	0
S₅	−0.00003216	−0.00001072	−0.00003216	0
S₆	260428016091	−67162084306	−5.19615242	38776047452.94
S₇	−26043446442	−67162915693	5.196152427	−38776527455.9

	x	y	z	w
S₈	−3899109.2976	−2598.3098032	5.1978846064	−1500.63494764
S₉	3902904.93013	2599.57438182	−5.197883763	−1501.36505241
S₁₀	0.00126415720	0.00042138576	0.0012641572	0.000000059188

Test image	Plain image			Cipher image
Test image	Horizontal	Vertical	Diagonal	Horizontal	Vertical	Diagonal
Lena (proposed)	0.99570	0.98470	0.99080	−0.00570	0.00160	0.00210
Lena (Ref. [17])	0.97190	0.94260	0.91990	0.01020	0.00670	0.00520
Lena (Ref. [20])	0.96457	0.97864	0.95098	−0.02457	−0.02264	−0.01930
Cameraman	0.99290	0.98040	0.98810	0.00590	0.00800	−0.00170
Girl	0.99620	0.98970	0.99270	0.00830	0.00520	−0.00460

Test image	Plaintext image	Ciphertext image
Lena (proposed)	7.39820	7.96920
Lena (Ref. [17])	−	7.99740
Lena (Ref. [20])	7.43087	7.98859
Cameraman	7.00060	7.96820
Girl	7.49570	7.98780

Memristor-based hyper-chaotic circuit for image encryption

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Test image	NPCR/%	UACI/%	BACI/%
Lena	99.62	33.42	26.73
Cameraman	99.59	33.54	26.79
Girl	99.60	33.43	26.76

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