Memristor-based hyper-chaotic circuit for image encryption

doi:10.1088/1674-1056/abbbfe

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.

Keywords: memristor SPICE simulation hyper-chaotic system image encryption

Received: 30 April 2020
Revised: 04 September 2020
Accepted manuscript online: 28 September 2020

Fund: 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).

Corresponding Authors: ^†Corresponding author. E-mail: ldwang@swu.edu.cn

Cite this article:

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 2020 Chin. Phys. B 29 110504

Fig. 1.

Phase portraits of system (1) with a = 3, b = 1, c = 9, e = 0.2, m = 1 in (a) x–y plane, (b) y–z plane, (c) x–z plane, and (d) x–w plane.

Table 1.

Equilibrium points of formula (5) when x < C₅.

Table 2.

Equilibrium points of formula (4) when C₅ ≤ x ≤ C₆.

Table 3.

Equilibrium points of formula (5) when x > C₆.

Fig. 2.

Poincare map of (a) x = 0 and (b) y = 0.

Fig. 3.

Lyapunov exponents of the system with a = 3, b = 1, c = 9, e = 0.2, m = 1.

Fig. 4.

Power spectrum of the system.

Fig. 5.

Time domain waveform of (a) t–y and (b) t–w.

Fig. 6.

Hardware circuit implementation of new hyper-chaotic system.

Fig. 7.

SPICE simulation results in (a) x–y, (b) y–z, (c) x–z, and (d) x–w planes of the system.

Fig. 8.

Block diagram of proposed image encryption.

Fig. 9.

Plain image of (a) Lena, (b) Cameraman, and (c) Girl; first encrypted image of (d) Lena, (e) Cameraman, and (f) Girl.

Fig. 10.

Second encrypted image of (a) Lena, (b) Cameraman, and (c) Girl; decrypted image of (d) Lena, (e) Cameraman, and (f) Girl.

Fig. 11.

Gray histogram of plaintext of (a) Lena, (b) Cameraman, (c) Girl; gray histogram of ciphered image of (d) Lena, (e) Cameraman, and (f) Girl.

Fig. 12.

Correlation distribution of (a) plaintext and (b) ciphertext image in horizontal, vertical, and diagonal direction of Lena.

Fig. 13.

Correlation distribution of (a) plaintext and (b) ciphertext image in horizontal, vertical, and diagonal direction of Cameraman.

Fig. 14.

Correlation distribution of (a) plaintext and (b) ciphertext image in horizontal, vertical, and diagonal direction of Girl.

Table 4.

Correlation coefficients of plain image and cipher image.

Table 5.

Information entropy of test images.

Table 6.

Values of NPCR, UACI, and BACI of different images after modifying one pixel value.

[1]	Lorenz E N 1963 J. Atmos. Sci. 20 130 DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[2]	Chen G R 1999 Int. J. Bifurcat. Chaos. 9 1465 DOI: 10.1142/S0218127499001024
[3]	Bao B C, Liu Z, Xu J P 2009 J. Syst. Eng. Electron. 20 1179 http://www.jseepub.com//EN/abstract/abstract8442.shtml
[4]	Xiao Y Q, Wang Z Y, Cao J, Long C X, Chen Y T, Deng R, Shi J, Liu Y 2019 Opt. Commun. 440 126 DOI: 10.1016/j.optcom.2019.02.033
[5]	Chua L O 1971 IEEE Trans. Circ. Theor. 18 507 DOI: 10.1109/TCT.1971.1083337
[6]	Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80 DOI: 10.1038/nature06932
[7]	Yang Y C, Pan F, Liu Q, Liu M, Zeng F 2009 Nano. Lett. 9 1636 DOI: 10.1021/nl900006g
[8]	Shin S H, Kyungmin Kim, Kang S M 2010 IEEE Trans. 10 1536
[9]	Itoh M, Chua L O 2008 Int. J. Bifurcat. Chaos 18 3183 DOI: 10.1142/S0218127408022354
[10]	Kyprianidis I M, Volos Ch K, Stouboulos I N 2010 AIP Conf. Proc. 1203 626 DOI: 10.1063/1.3322524
[11]	Stork M, Hrusak J, Mayer D 2009 Electrical and Electronics Engineering December 2009 https://www.researchgate.net/publication/224091520_Feedback_systems_with_memristors
[12]	Yang D W, Wang L D, Duan S K 2018 Acta Phys. Sin. 67 110502 in Chinese DOI: 10.7498/aps.67.20180025
[13]	Lv Y W, Min F H 2019 Acta Phys. Sin. 68 130502 in Chinese DOI: 10.7498/aps.68.20190453
[14]	Wang M J, Deng Y, Liao X H, Li Z J, Ma M L, Zeng Y C 2019 Int. J. Nonlinear Mech. 111 149 DOI: 10.1016/j.ijnonlinmec.2019.02.009
[15]	Li C H, Luo G C, Qin K 2017 Nonlinear Dyn. 87 127 DOI: 10.1007/s11071-016-3030-8
[16]	Wang X Y, Wang Y, Wang S W, Zhang Y Q, Wu X J 2018 Chin. Phys. B 27 110502 DOI: 10.1088/1674-1056/27/11/110502
[17]	Ye X L, Wang X Y, Gao S, Mou J, Wang Z S, Yang F F 2019 Nonlinear Dyn. 99 1489 DOI: 10.1007/s11071-019-05370-2
[18]	Wang L M, Dong T D, Ge M F 2019 Appl. Math. Comput. 347 293 DOI: 10.1109/ACCESS.2018.2872745
[19]	Zhang Y, Tang Y J 2017 Multimed. Tools Appl. 77 6647 DOI: 10.1007/s11042-017-4577-1
[20]	Yang F F, Mou J, Sun K H, Cao Y H, Jin J Y 2019 IEEE Access DOI: 10.1109/ACCESS.2019.2914722
[21]	Zhang L M, Sun K H, Liu W H, He S B 2017 Chin. Phys. B 26 100504 DOI: 10.1088/1674-1056/26/10/100504
[22]	Wang B, Zou F C, Cheng J 2018 Optik 154 538 DOI: 10.1016/j.ijleo.2017.10.080
[23]	Wang X Y, Xie Y X, Qin X 2012 Chin. Phys. B 21 040504 DOI: 10.1088/1674-1056/21/4/040504
[24]	Wang Z L, Min F H, Wang E R 2016 AIP Adv. 6 095316 DOI: 10.1063/1.4963743
[25]	Shi H, Wang L D 2019 Acta Phys. Sin. 68 200501 in Chinese DOI: 10.7498/aps.68.20190553
[26]	Zhang Y 2016 Chaos digital image encryption 1 Beijing Tsinghua University Press 218 in Chinese https://xueshu.baidu.com/usercenter/paper/show?paperid=380477c17efa30de7e91325902f70850&site=xueshu_se

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