Abstract:In order to make the chaotic sequence show more complex characteristics, a piecewise linear function is introduced into the typical Chua’s system to produce a controllable number of multi-scroll attractors. The dynamic analysis of this system is performed, and the results illustrate that the chaotic characteristics of the system are widely distributed and have rich dynamic behaviors. On this basis, an encryption algorithm based on Zigzag scrambling and DNA coding is proposed, and its security is analyzed from multiple aspects. The simulation results indicate that this method can not only encrypt the image effectively, but also resist a variety of common attacks effectively, which provides a theoretical basis for image encryption.
刘思洋, 安新磊, 施倩倩, 王越. 一类多涡卷Chua系统及其在图像加密中的应用[J]. 复杂系统与复杂性科学, 2024, 21(3): 85-92.
LIU Siyang, AN Xinlei, SHI Qianqian, WANG Yue. A Multi-scroll Chua System and Its Application in Image Encryption[J]. Complex Systems and Complexity Science, 2024, 21(3): 85-92.
[1] 王雪荣, 刘浩. 5G框架下数字图像加密技术的发展趋势[J]. 广东通信技术, 2019, 39(8): 2-4. WANG X R, LIU H. Development trend of digital image encryption technology under 5G framework[J]. Guangdong Communication Technology, 2019, 39(8): 2-4. [2] DU F Y, SHEN Q H, DONG W J, et al. An image encryption system based on chaos principle[C]//2022 IEEE 2nd International Conference on Electronic Technology, Communication and Information (ICETCI), Changchun, China: IEEE, 2022: 162-167. [3] 禹思敏, 林清华, 丘水生. 四维系统中多涡卷混沌与超混沌吸引子的仿真研究[J]. 物理学报, 2003(1): 25-33. YU S M, LIN Q H, QIU SS. Simulation investigation on multi-scroll chaotic and hyperchaotic attractors for four-dimensional systems[J]. Acta Physica Sinica, 2003(1): 25-33. [4] 贾美美, 蒋浩刚, 李文静. 新Chua多涡卷混沌吸引子的产生及应用[J]. 物理学报, 2019, 68(13): 61-73. JIA MM, JIANG H G, LI W J. Generation and application of novel Chua multi-scroll chaotic attractors[J]. Acta Physica Sinica, 2019, 68(13): 61-73. [5] SAHOO S, ROY B K. Design of multi-wing chaotic systems with higher largest Lyapunov exponent[J]. Chaos, Solitons and Fractals, 2022, 157: 111926. [6] ZHANG S, ZHENG J, WANG X, et al. Multi-scroll hidden attractor in memristive HR neuron model under electromagnetic radiation and its applications[J]. Chaos: an Interdisciplinary Journal of Nonlinear Science, 2021, 31(1): 011101. [7] 安新磊, 熊丽, 乔帅. 电磁驱动下一类混合神经元模型的动力学响应与图像加密应用[J]. 电子与信息学报, 2022, 44: 1-12. AN X L, XIONG L, QIAO S. Dynamic response of a class of hybrid neuron model by electromagnetic induction and application of image encryption[J]. Journal of Electronics & Information Technology, 2022, 44: 1-12. [8] 摆玉龙, 杨阳, 唐丽红. 一个新多涡卷混沌系统的设计及在图像加密中的应用[J]. 电子与信息学报, 2021, 43(02): 436-444. BAI Y L, YANG Y, TANG L H. Design of a multi-scroll chaotic system and its application to image encryption[J]. Journal of Electronics & Information Technology, 2021, 43(2): 436-444. [9] DEMIRTAS M. A new RGB color image encryption scheme based on cross-channel pixel and bit scrambling using chaos[J]. Optik, 2022, 265: 169430. [10] 王永, 龚建, 王明月. 基于三维分段Sine映射的彩色图像加密[J]. 北京理工大学学报, 2022, 42(4): 415-423. WANG Y, GONG J, WANG M Y. Color image encryption based on three-dimensional piecewise sine map[J]. Transactions of Beijing Institute of Technology, 2022, 42(4): 415-423. [11] 刘思聪, 李春彪, 李泳新. 基于指数-余弦离散混沌映射的图像加密算法研究[J]. 电子与信息学报, 2022, 44(5): 1754-1762. LIU S C, LI C B, LI Y X. A novel image encryption algorithm based on exponent-cosine chaotic mapping[J]. Journal of Electronics & Information Technology, 2022, 44(5): 1754-1762. [12] 张昊, 王晓庆, 谢红薇, 等. 基于SCC映射的彩色图像分块压缩加密算法[J]. 计算机工程与设计, 2022, 43(7): 1801-1809. ZHANG H, WANG X Q, XIE H W, et al. Block compression-encryption algorithm for color images coupling SCC chaotic map[J]. Computer Engineering and Design, 2022, 43(7): 1801-1809. [13] HUA Z Y, ZHOU Y C, HUANG H J. Cosine-transform-based chaotic system for image encryption[J]. Information Sciences, 2019, 480: 403-419. [14] SHI Q Q, AN X L, XIONG L. Dynamic analysis of fractional- order hyperchaotic system and its application in image encryption[J]. Physica Scripta, 2022, 97(4): 045201. [15] YANG F F, MOU J, LUO C F, et al. An improved color image encryption scheme and cryptanalysis based on a hyperchaotic sequence[J]. Physica Scripta, 2019, 94(8): 085206. [16] ZAREBNIA M, PARVAZ R. Image encryption algorithm by fractional based chaotic system and framelet transform[J]. Chaos, Solitons and Fractals, 2021, 152: 111402. [17] DONG H, BAI E, JIANG X Q, et al. Color image compression-encryption using fractional-order hyperchaotic system and DNA coding[J]. IEEE Access, 2020, 8: 163524-163540. [18] WU X, WANG K, WANG X, et al. Color image DNA encryption using NCA map-based CML and one-time keys[J]. Signal Processing, 2018, 148: 272-287. [19] 方鹏飞, 黄陆光, 娄苗苗, 等. 基于四维超混沌系统的彩色图像加密算法[J]. 计算机工程与设计, 2022, 43(2): 361-369. FANG P F, HUNAG L G, LOU M M. Color image encryption algorithm based on four dimensional hyperchaotic system[J]. Computer Engineering and Design, 2022, 43(2): 361-369. [20] CHUA L, KOMURO M, MATSUMOTO T. The double scroll family[J]. IEEE Transactions on Circuits and Systems, 1986, 33(11): 1072-1118. [21] WATSON J D, CRICK F H C. Molecular structure of nucleic acids: a structure for deoxyribose nucleic acid[J]. Nature, 1953, 171(4356): 737-738.