Dynamics analysis of chaotic maps: From perspective on parameter estimation by meta-heuristic algorithm

doi:10.1088/1674-1056/ab695c

Abstract Chaotic encryption is one of hot topics in cryptography, which has received increasing attention. Among many encryption methods, chaotic map is employed as an important source of pseudo-random numbers (PRNS). Although the randomness and the butterfly effect of chaotic map make the generated sequence look very confused, its essence is still the deterministic behavior generated by a set of deterministic parameters. Therefore, the unceasing improved parameter estimation technology becomes one of potential threats for chaotic encryption, enhancing the attacking effect of the deciphering methods. In this paper, for better analyzing the cryptography, we focus on investigating the condition of chaotic maps to resist parameter estimation. An improved particle swarm optimization (IPSO) algorithm is introduced as the estimation method. Furthermore, a new piecewise principle is proposed for increasing estimation precision. Detailed experimental results demonstrate the effectiveness of the new estimation principle, and some new requirements are summarized for a secure chaotic encryption system.

Keywords: parameter estimation chaotic map particle swarm optimization chaotic encryption

Received: 06 October 2019
Revised: 26 November 2019
Accepted manuscript online:

PACS:	05.45.Gg	(Control of chaos, applications of chaos)
	05.45.Pq	(Numerical simulations of chaotic systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61161006 and 61573383), the Key Innovation Project of Graduate of Central South University (Grant No. 2018ZZTS009), and the Postdoctoral Innovative Talents Support Program (Grant No. BX20180386).

Corresponding Authors: Ke-Hui Sun
E-mail: kehui@csu.edu.cn

Cite this article:

Yue-Xi Peng(彭越兮), Ke-Hui Sun(孙克辉), Shao-Bo He(贺少波) Dynamics analysis of chaotic maps: From perspective on parameter estimation by meta-heuristic algorithm 2020 Chin. Phys. B 29 030502

[1]	Pecora L and Carroll T 1990 Phys. Rev. Lett. 64 821
[2]	Zhang Z, Feng X, Yao Z, et al. 2015 Chin. Phys. B 24 110503
[3]	Roy A and Misra A 2017 Euro. Phys. J. Plus 132 524
[4]	Altaf M, Ahmad A, Khan F, et al. 2017 Multimed. Tools Appl. 77 27981
[5]	Azzaz M, Tanougast C, Sadoudi S, et al. 2013 Commun. Nonlinear Sci. 18 2035
[6]	Sheu L 2011 Nonlinear Dyn. 1-2 103
[7]	Liu Z, Xia T and Wang J 2018 Chin. Phys. B 27 030502
[8]	Chen Y, Wang J, Chen X, et al. 2019 IEEE Access 7 58791
[9]	Cheng G, Wang C and Chen H, et al. 2019 Int. J. Bifur. Chaos 29 1950115
[10]	Yin Q and Wang C 2018 Int. J. Bifur. Chaos 28 1850047
[11]	Wang X, Wang Q and Zhang Y 2015 Nonlinear Dyn. 79 1141
[12]	Asgari-Chenaghlu M, Balafar M A and Feizi-Derakhshi M R 2019 Signal Process. 57 1
[13]	Wu Y, Noonan J, Yang G, et al. 2012 J. Electron. Imaging 21 013014
[14]	Xie Y, Li J, Kong Z, et al. 2016 J. Lightwave Technol. 34 5101
[15]	Hua Z, Zhou Y, Pun C M, et al. 2015 Inform. Sci. 297 80
[16]	Hua Z and Zhou Y 2016 Inform. Sci. 339 237
[17]	Liu W, Sun K and Zhu C 2016 Opt. Laser Eng. 84 26
[18]	Cao C, Sun K and Liu W 2018 Signal Process. 143 122
[19]	Nepomuceno E, Nardo L, Arias-Garcia J, et al. 2019 Chaos 29 061101
[20]	Li C, Lin D, Lü J, et al. 2018 IEEE T. Multimedia 25 46
[21]	Mao Y and Chen G 2005 Chaos-Based Image Encryption (Berlin: Springer)
[22]	Wang N, Li C, Bao H, et al. 2019 IEEE T. Circuit-I 66 4767
[23]	Hua Z, Zhou Y and Bao B 2019 IEEE T. Ind. Inform. 480 403
[24]	Li C, Feng B, Li S, et al. 2019 IEEE T. Circuit-I 66 2322
[25]	Li C, Lin D, Feng B, et al. 2018 IEEE Access 6 75834
[26]	Peng H, Li L, Yang Y, et al. 2010 Phys. Rev. E 81 016207
[27]	Zheng S, Wang J, Zhou S, et al. 2014 Chaos 24 013133
[28]	Lazzús J, Rivera M and López-Caraballo C 2016 Phys. Lett. A 380 1164
[29]	Peng Y, Sun K, He S, et al. 2018 Eur. Phys. J. Plus 133 305
[30]	Xu S, Wang Y and Liu X 2018 Neural Comput. Appl. 30 2607
[31]	Yousri D, AbdelAty A, Said L, et al. 2019 Nonlinear Dyn. 95 2491
[32]	Du W, Miao Q, Tong L, et al. 2017 Phys. Lett. A 381 1943
[33]	Peng Y, Sun K, He S, et al. 2019 Entropy 21 27
[34]	Peng Y, Sun K, He S, et al. 2019 Mod. Phys. Lett. B 33 1950041
[35]	Wang D, Tan D and Liu L 2018 Soft Comput. 22 387
[36]	Wang G and Yuan F 2013 Acta Phys. Sin. 62 020506 (in Chinese)
[37]	Lee T F 2018 IEEE Syst. J. 12 1499
[38]	Ginelli F, Poggi P, Turchi A, et al. 2007 Phys. Rev. Lett. 99 130601

[1]	Feedback control and quantum error correction assisted quantum multi-parameter estimation Hai-Yuan Hong(洪海源), Xiu-Juan Lu(鲁秀娟), and Sen Kuang(匡森). Chin. Phys. B, 2023, 32(4): 040603.
[2]	A color image encryption algorithm based on hyperchaotic map and DNA mutation Xinyu Gao(高昕瑜), Bo Sun(孙博), Yinghong Cao(曹颖鸿), Santo Banerjee, and Jun Mou(牟俊). Chin. Phys. B, 2023, 32(3): 030501.
[3]	Asymmetric image encryption algorithm based ona new three-dimensional improved logistic chaotic map Guo-Dong Ye(叶国栋), Hui-Shan Wu(吴惠山), Xiao-Ling Huang(黄小玲), and Syh-Yuan Tan. Chin. Phys. B, 2023, 32(3): 030504.
[4]	Environmental parameter estimation with the two-level atom probes Mengmeng Luo(罗萌萌), Wenxiao Liu(刘文晓), Yuetao Chen(陈悦涛), Shangbin Han(韩尚斌), and Shaoyan Gao(高韶燕). Chin. Phys. B, 2022, 31(5): 050304.
[5]	Parameter estimation of continuous variable quantum key distribution system via artificial neural networks Hao Luo(罗浩), Yi-Jun Wang(王一军), Wei Ye(叶炜), Hai Zhong(钟海), Yi-Yu Mao(毛宜钰), and Ying Guo(郭迎). Chin. Phys. B, 2022, 31(2): 020306.
[6]	A novel hyperchaotic map with sine chaotification and discrete memristor Qiankun Sun(孙乾坤), Shaobo He(贺少波), Kehui Sun(孙克辉), and Huihai Wang(王会海). Chin. Phys. B, 2022, 31(12): 120501.
[7]	Blind parameter estimation of pseudo-random binary code-linear frequency modulation signal based on Duffing oscillator at low SNR Ke Wang(王珂), Xiaopeng Yan(闫晓鹏), Ze Li(李泽), Xinhong Hao(郝新红), and Honghai Yu(于洪海). Chin. Phys. B, 2021, 30(5): 050708.
[8]	Quantum estimation of detection efficiency with no-knowledge quantum feedback Dong Xie(谢东), Chunling Xu(徐春玲). Chin. Phys. B, 2018, 27(6): 060303.
[9]	Quantum parameter estimation in a spin-boson dephasing quantum system by periodical projective measurements Le Yang(杨乐), Hong-Yi Dai(戴宏毅), Ming Zhang(张明). Chin. Phys. B, 2018, 27(4): 040601.
[10]	Particle swarm optimization and its application to the design of a compact tunable guided-mode resonant filter Dan-Yan Wang(王丹燕), Qing-Kang Wang(王庆康). Chin. Phys. B, 2018, 27(3): 037801.
[11]	Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem Zeyu Liu(刘泽宇), Tiecheng Xia(夏铁成), Jinbo Wang(王金波). Chin. Phys. B, 2018, 27(3): 030502.
[12]	Quantum metrology with a non-Markovian qubit system Jiang Huang(黄江), Wen-Qing Shi(师文庆), Yu-Ping Xie(谢玉萍), Guo-Bao Xu(徐国保), Hui-Xian Wu(巫慧娴). Chin. Phys. B, 2018, 27(12): 120301.
[13]	Modulating quantum Fisher information of qubit in dissipative cavity by coupling strength Danping Lin(林丹萍), Yu Liu(刘禹), Hong-Mei Zou(邹红梅). Chin. Phys. B, 2018, 27(11): 110303.
[14]	Structural optimization of Au-Pd bimetallic nanoparticles with improved particle swarm optimization method Gui-Fang Shao(邵桂芳), Meng Zhu(朱梦), Ya-Li Shangguan(上官亚力), Wen-Ran Li(李文然), Can Zhang(张灿), Wei-Wei Wang(王玮玮), Ling Li(李玲). Chin. Phys. B, 2017, 26(6): 063601.
[15]	Inverse full state hybrid projective synchronizationfor chaotic maps with different dimensions Adel Ouannas, Giuseppe Grassi. Chin. Phys. B, 2016, 25(9): 090503.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Dynamics analysis of chaotic maps: From perspective on parameter estimation by meta-heuristic algorithm

Cite this article:

Online attention