Please wait a minute...
Chin. Phys. B, 2012, Vol. 21(5): 050506    DOI: 10.1088/1674-1056/21/5/050506
GENERAL Prev   Next  

Image encryption based on a delayed fractional-order chaotic logistic system

Wang Zhen(王震)a), Huang Xia(黄霞) b)†, Li Ning(李宁)a), and Song Xiao-Na(宋晓娜)c)
a. College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China;
b. Key Laboratory of Robotics and Intelligent Technology, College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266590, China;
c. College of Electronic and Information Engineering, Henan University of Science and Technology, Luoyang 471003, China
Abstract  A new image encryption scheme is proposed based on a delayed fractional-order chaotic logistic system. In the process of generating a key stream, the time-varying delay and fractional derivative are embedded in the proposed scheme to improve the security. Such a scheme is described in detail with security analyses including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. Experimental results show that the newly proposed image encryption scheme possesses high security.
Keywords:  image encryption      fractional-order chaotic logistic system      delay  
Received:  09 October 2011      Revised:  27 April 2012      Accepted manuscript online: 
PACS:  05.45.Gg (Control of chaos, applications of chaos)  
  05.45.Vx (Communication using chaos)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61004078 and 60971022), the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2009GQ009 and ZR2009GM005), the China Postdoctoral Science Foundation, and the Special Funds for Postdoctoral Innovative Projects of Shandong Province, China.

Cite this article: 

Wang Zhen(王震), Huang Xia(黄霞), Li Ning(李宁), and Song Xiao-Na(宋晓娜) Image encryption based on a delayed fractional-order chaotic logistic system 2012 Chin. Phys. B 21 050506

[1] Yu W W and Cao J D 2006 Phys. Lett. A 356 333
[2] Wang K, Pei W J, Zhou J T, Zhang Y F and Zhou S Y 2011 Acta Phys. Sin. 60 070503 (in Chinese)
[3] Tang Y, Wang Z D and Fang J A 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 2456
[4] Tong X J and Cui M G 2009 Signal Process. 89 480
[5] Pareek N K, Patidar V and Sud K K 2006 Image Vision Comput. 24 926
[6] Kocarev L and Jakimoski G 2001 Phys. Lett. A 289 199
[7] Pareek N K, Patidar V and Sud K K 2005 Commun. Nonlinear Sci. Numer. Simulat. 10 715
[8] Yang T, Wu C W and Chua L O 1997 IEEE Trans. Circuits Syst. I 44 469
[9] Alvarez G and Li S 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 3743
[10] Wang X Y and Zhao J F 2010 Neurocomputing 73 3224
[11] Akhshani A, Behnia S, Akhavan A, Hassan H A and Hassan Z 2010 Opt. Commun. 283 3259
[12] Kiani-B A, Fallahi K, Pariz N and Leung H 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 863
[13] Schneier B 1996 Applied Cryptography (New York:John Wiley & Sons)
[14] Chang C C, Hwang M S and Chen T S 2001 J. Syst. Software 58 83
[15] Shannon C E 1949 Bell System Technical J. 28 656
[16] Fridrich J 1998 Int. J. Bifurcation and Chaos 8 1259
[17] Kocarev L 2001 IEEE Cir. Syst. Mag. 1 6
[18] Podlubny I 1999 Fractional Differential Equations (New York:Academic)
[19] Heaviside O 1971 Electromagnetic Theory (New York:Chelsea)
[20] Hartley T T, Lorenzo C F and Qammer H K 1995 IEEE Trans. Circuits Syst. I 42 485
[21] Zhang R X and Yang S P 2009 Acta Phys. Sin. 58 2957 (in Chinese)
[22] Zhang R X and Yang S P 2009 Chin. Phys. B 18 3295
[23] Liu Y and Xie Y 2010 Acta Phys. Sin. 59 2147 (in Chinese)
[24] Yu Y G, Li H X, Wang S and Yu J Z 2009 Chaos Soliton. Fract. 42 1181
[25] Li C P and Chen G R 2004 Physica A 341 55
[26] Varsha D and Sachin B 2010 Comput. Math. Appl. 59 1117
[27] Lu J G 2005 Chaos Soliton. Fract. 26 1125
[28] Podlubny I 2002 J. Fract. Calc. 5 367
[29] Wang Z, Huang X and Shi G D 2011 Comput. Math. Appl. 62 1531
[30] Ponomarenko V I and Prokhorov M D 2002 Phys. Rev. E 66 026215
[31] Wang Z and Huang X 2012 Applied Mathematics & Information Science (accepted)
[32] Wang D P and Yu J B 2008 J. Electron. Sci. Tech. 6 289
[33] Behnia S, Akhshani A, Akhavan A and Mahmpdi H 2009 Chaos Soliton. Fract. 40 505
[34] Zhang X F and Fan J L 2010 Comput. Sci. 2 264 (in Chinese)
[1] 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.
[2] Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays
Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Chin. Phys. B, 2023, 32(3): 038701.
[3] Effect of autaptic delay signal on spike-timing precision of single neuron
Xuan Ma(马璇), Yaya Zhao(赵鸭鸭), Yafeng Wang(王亚峰), Yueling Chen(陈月玲), and Hengtong Wang(王恒通). Chin. Phys. B, 2023, 32(3): 038703.
[4] 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.
[5] Lossless embedding: A visually meaningful image encryption algorithm based on hyperchaos and compressive sensing
Xing-Yuan Wang(王兴元), Xiao-Li Wang(王哓丽), Lin Teng(滕琳), Dong-Hua Jiang(蒋东华), and Yongjin Xian(咸永锦). Chin. Phys. B, 2023, 32(2): 020503.
[6] Synchronously scrambled diffuse image encryption method based on a new cosine chaotic map
Xiaopeng Yan(闫晓鹏), Xingyuan Wang(王兴元), and Yongjin Xian(咸永锦). Chin. Phys. B, 2022, 31(8): 080504.
[7] Exponential sine chaotification model for enhancing chaos and its hardware implementation
Rui Wang(王蕊), Meng-Yang Li(李孟洋), and Hai-Jun Luo(罗海军). Chin. Phys. B, 2022, 31(8): 080508.
[8] Neural-mechanism-driven image block encryption algorithm incorporating a hyperchaotic system and cloud model
Peng-Fei Fang(方鹏飞), Han Liu(刘涵), Cheng-Mao Wu(吴成茂), and Min Liu(刘旻). Chin. Phys. B, 2022, 31(4): 040501.
[9] Review on typical applications and computational optimizations based on semiclassical methods in strong-field physics
Xun-Qin Huo(火勋琴), Wei-Feng Yang(杨玮枫), Wen-Hui Dong(董文卉), Fa-Cheng Jin(金发成), Xi-Wang Liu(刘希望), Hong-Dan Zhang(张宏丹), and Xiao-Hong Song(宋晓红). Chin. Phys. B, 2022, 31(3): 033101.
[10] Inferring interactions of time-delayed dynamic networks by random state variable resetting
Changbao Deng(邓长宝), Weinuo Jiang(蒋未诺), and Shihong Wang(王世红). Chin. Phys. B, 2022, 31(3): 030502.
[11] Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation
Wenjie Yang(杨文杰). Chin. Phys. B, 2022, 31(2): 020201.
[12] FPGA implementation and image encryption application of a new PRNG based on a memristive Hopfield neural network with a special activation gradient
Fei Yu(余飞), Zinan Zhang(张梓楠), Hui Shen(沈辉), Yuanyuan Huang(黄园媛), Shuo Cai(蔡烁), and Sichun Du(杜四春). Chin. Phys. B, 2022, 31(2): 020505.
[13] An image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree
Yining Su(苏怡宁), Xingyuan Wang(王兴元), and Shujuan Lin(林淑娟). Chin. Phys. B, 2022, 31(11): 110503.
[14] Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application
Yong-Bing Hu(胡永兵), Xiao-Min Yang(杨晓敏), Da-Wei Ding(丁大为), and Zong-Li Yang(杨宗立). Chin. Phys. B, 2022, 31(11): 110501.
[15] Finite-time Mittag—Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay
Guan Wang(王冠), Zhixia Ding(丁芝侠), Sai Li(李赛), Le Yang(杨乐), and Rui Jiao(焦睿). Chin. Phys. B, 2022, 31(10): 100201.
No Suggested Reading articles found!