Image Encryption Algorithm Based on a Four-dimensional Memristor Hyperchaotic System
YAN Shaohui, GU Binxiana, SONG Zhenlonga, SHI Wanlina
a. College of Physics and Electronic Engineering;b. Engineering Research Center of Gansu Province for Intelligent Information Technology and Application, Northwest Normal University, Lanzhou 730070, China
Abstract：The image encryption algorithm based on low dimensional chaotic system has the problems of the key space small and the security not high. In this paper, an improved four-dimensional Lorenz dissipative hyperchaotic system is constructed by introducing a cubic smooth memristor model. The dynamic characteristics of the improved system such as phase portraits, dissipation, equilibrium stability, Lyapunov exponent, and bifurcation are investigated, it is proved that the system has good dynamic characteristics and chaotic attractor. Therefore, a chaotic sequence encryption algorithm based on Hash algorithm is proposed. By histogram, key space analysis,robust analysis and other verifications show that the image encryption algorithm has higher key space and can resist brute-force attack.
闫少辉, 顾斌贤, 宋震龙, 施万林. 基于一种四维忆阻超混沌系统的图像加密算法[J]. 复杂系统与复杂性科学, 2023, 20(2): 43-51.
YAN Shaohui, GU Binxian, SONG Zhenlong, SHI Wanlin. Image Encryption Algorithm Based on a Four-dimensional Memristor Hyperchaotic System. Complex Systems and Complexity Science, 2023, 20(2): 43-51.
[1] CHUA L O. Memristor the missing circuit element [J]. IEEE Trans Circuit Theory,1971,18(5):507-519. [2] CHUA L O, KANG S M. Memristive devices and systems[J]. Proc IEEE, 1976, 64(2):209-223. [3] ZHANG Y, WANG X, FRIEDMAN E G. Memristor-based circuit design for multilayer neural networks[J]. IEEE Transactions on Circuits and Systems Part 1 Regular Papers, 2018, 65(2):677-686. [4] GAO C, LI T, CAO X, et al. Identification circuit based on memristor[J]. Journal of Physics Conference Series, 2021, 1827(1):012007. [5] SHCHANIKOV S, ZUEV A, BORDANOV I, et al. Design and simulation of memristor-based artificial neural network for bidirectional adaptive neural interface[DB/OL].[2021-06-01]. https://arxiv.org/abs/2004.00154. [6] LUO L, HU X, DUAN S, et al. Multiple memristor series-parallel connections with use in synaptic circuit design[J]. Iet Circuits Devices & Systems, 2017, 11(2):123-134. [7] MATTHEWS R. On the derivation of a "Chaotic" encrypt- ion algorithm[J]. Cryptologia, 1989, 13(1):29-41. [8] YANG S. Dynamical analysis and image encryption application of a novel memristive hyperchaotic system[J]. Optics & Laser Technology, 2021, 133(1):106553. [9] 汪彦, 涂立. 基于改进Lorenz混沌系统的图像加密新算法[J]. 中南大学学报(自然科学版),2017,48(10): 2678-2685. WANG Y, TU L. A new image encryption algorithm based on improved Lorenz chaotic system[J]. Journal of Central South University (Science and Technology), 2017, 48(10): 2678- 2685. [10] 谢国波, 姜先值. 二维离散分数阶Fourier变换的双混沌图像加密算法[J]. 计算机工程与应用,2018, 54(3):40-45. XIE G B, JIANG X Z. Double chaotic image encryption algorithm based on two dimensional discrete fractional fourier transform[J]. Computer Engineering and Applications, 2018, 54(3):40-45. [11] 朱淑芹, 李俊青. 一种混沌图像加密算法的选择明文攻击和改进[J]. 计算机工程与应用,2017,53(24):113-121. ZHU S Q, LI G Q. Chosen plain text attack and improvements of chaos image encryption algorithm[J]. Computer Engineering and Applications, 2017, 53(24): 113-121. [12] 付正, 李嵘. 基于新型切换Lorenz混沌系统的图像加密算法研究[J]. 计算机与数字工程,2020, 48(1):170-173. FU Z, LI R. Application of a switched lorenz chaotic system in image encryption[J]. Computer & Digital Engineering, 2020, 48 (1):170-173. [13] 张永红, 张博. 基于Logistic混沌系统的图像加密算法研究[J]. 计算机应用研究,2015, 32(6):1770-1773. ZHANG Y H, ZHANG B. Algorithm of image encrypting based on Logistic chaotic system[J]. Application Research of Computers, 2015, 32 (6): 1770 -1773. [14] 王静, 蒋国平. 一种超混沌图像加密算法的安全性分析及其改进[J]. 物理学报,2011,66(6):89-99. WANG J, JIANG G P. Cryptanalysis of a hyper-chaotic image encryption algorithm and its improved version[J]. Acta Phys Sin,2011,66(6):89-99. [15] 李伟岸, 熊祥光, 夏道勋. 基于超混沌和Slant变换的鲁棒水印算法[J]. 计算机工程与科学,2020, 42(5):55-61. LI W A, XIONG X G, XIA D X. A robust watermarking algorithm based on hyper-chaotic and Slant transform[J]. Computer Engineering & Science,2020,42(5):55-61. [16] 程东升, 谭旭, 许志良,等. 结合四维超混沌系统和位分解的图像加密算法研究[J]. 电子科技大学学报, 2018, 47(6):108-114. CHENG D S, TAN X, XU Z L, et al. Image encryption algorithm research by combining four dimensional hyper-chaotic system and bit decomposition [J]. Journal of University of Electionic Science and Technology of China, 2018, 47(6):108-114. [17] 阮静雅, 孙克辉, 牟俊. 基于忆阻器反馈的Lorenz超混沌系统及其电路实现[J]. 物理学报, 2016, 65(19): 190502. RUAN J Y, SUN K H, MOU J. Memeristor-based Lorenz hyper-chaotic system and its circuit implementation [J]. Acta Phys Sin, 2016,65(19): 190502. [18] 蔡国梁, 黄娟娟. 超混沌Chen系统和超混沌Rossler系统的异结构同步[J].物理学报,2006, 55(8):3997-4004. CAI G L, HUANG J J. Synchronization for hyperchaotic Chen system and hyperchaotic Rossler system with different structure [J]. Acta Phys Sin, 2006, 55(8):3997-4004. [19] YONG Z. The unified image encryption algorithm based on chaos and cubic S-Box[J]. Information Sciences, 2018, 450:361-377. [20] ALGREDO B I, FEREGRINO U C, CUMPLIDO R, et al. FPGA-based implementation alternatives for the inner loop of the secure hash algorithm SHA-256[J]. Microprocessors & Microsystems, 2013, 37(6/7):750-757. [21] SHAKIBA A randomized CPA-secure asymmetric color image encryption scheme based on the Chebyshev mappings and one-time pad [J]. Journal of King Saud University-Computer and Information Sciences, 2021, 33(5):562-571. [22] CHAI X L, FU X L, GAN Z H, et al. A color image cryptosystem based on dynamic DNA encryption and chaos[J]. Signal Processing, 2019, 155:44-62.
