An image encryption scheme based on three-dimensional Brownian motion and chaotic system

doi:10.1088/1674-1056/26/2/020504

Abstract At present, many chaos-based image encryption algorithms have proved to be unsafe, few encryption schemes permute the plain images as three-dimensional (3D) bit matrices, and thus bits cannot move to any position, the movement range of bits are limited, and based on them, in this paper we present a novel image encryption algorithm based on 3D Brownian motion and chaotic systems. The architecture of confusion and diffusion is adopted. Firstly, the plain image is converted into a 3D bit matrix and split into sub blocks. Secondly, block confusion based on 3D Brownian motion (BCB3DBM) is proposed to permute the position of the bits within the sub blocks, and the direction of particle movement is generated by logistic-tent system (LTS). Furthermore, block confusion based on position sequence group (BCBPSG) is introduced, a four-order memristive chaotic system is utilized to give random chaotic sequences, and the chaotic sequences are sorted and a position sequence group is chosen based on the plain image, then the sub blocks are confused. The proposed confusion strategy can change the positions of the bits and modify their weights, and effectively improve the statistical performance of the algorithm. Finally, a pixel level confusion is employed to enhance the encryption effect. The initial values and parameters of chaotic systems are produced by the SHA 256 hash function of the plain image. Simulation results and security analyses illustrate that our algorithm has excellent encryption performance in terms of security and speed.

Keywords: image encryption logistic-tent system (LTS) memristive chaotic system three-dimensional (3D) Brownian motion

Received: 03 August 2016
Revised: 26 November 2016
Accepted manuscript online:

PACS:	05.45.Gg	(Control of chaos, applications of chaos)
	05.45.-a	(Nonlinear dynamics and chaos)
	05.45.Vx	(Communication using chaos)
	05.40.Jc	(Brownian motion)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 41571417 and 61305042), the National Science Foundation of the United States (Grant Nos. CNS-1253424 and ECCS-1202225), the Science and Technology Foundation of Henan Province, China (Grant No. 152102210048), the Foundation and Frontier Project of Henan Province, China (Grant No. 162300410196), China Postdoctoral Science Foundation (Grant No. 2016M602235), the Natural Science Foundation of Educational Committee of Henan Province, China (Grant No. 14A413015), and the Research Foundation of Henan University, China (Grant No. xxjc20140006).

Corresponding Authors: Xiu-Li Chai
E-mail: chaixiuli@henu.edu.cn

Cite this article:

Xiu-Li Chai(柴秀丽), Zhi-Hua Gan(甘志华), Ke Yuan(袁科), Yang Lu(路杨), Yi-Ran Chen(陈怡然) An image encryption scheme based on three-dimensional Brownian motion and chaotic system 2017 Chin. Phys. B 26 020504

[1]	Zhang X Y, Zhang G J, Li Xuan, Ren Y Z and Wu J H 2016 Chin. Phys. B 25 054201
[2]	Luo Y L, Cao L C, Qiu S H, Lin H, Harkin Jim and Liu J X 2016 Nonlinear Dyn. 83 2293
[3]	Wang Z, Huang X, Li Y X and Song X N 2013 Chin. Phys. B 22 010504
[4]	Matthews R 1989 Cryptologia 4 29
[5]	Wang X Y and Wang Q 2014 Chin. Phys. B 23 030503
[6]	Zhou Y C, Hua Z Y, Pun C M and Philip Chen C L 2015 IEEE T. Cybernetics 45 2001
[7]	Ye G D 2014 Nonlinear Dyn. 75 417
[8]	Chai X L, Gan Z H, Chen Y R and Zhang Y S 2017 Signal Process. 134 35
[9]	Zhang Y Q and Wang X Y 2014 Inf. Sci. 273 329
[10]	Tong X J, Wang Z, Zhang M, Liu Y, Xu H and Ma J 2015 Nonlinear Dyn. 80 1493
[11]	Yen J C and Guo J I 2000 IEEE Proc. Vis. Image Signal Process. 147 167
[12]	Li C Q 2016 Signal Process. 118 203
[13]	Li H, Wang Y, Yan H, Li L, Li Q and Zhao Z 2013 Opt. Lasers Eng. 51 1327
[14]	Chen J X, Zhu Z L, Fu C, Zhang L B and Yu H 2015 Opt. Lasers Eng. 66 1
[15]	Liu Y S, Fan H, Xie Y Eric, Cheng G and Li C Q 2015 Int. J. Bifur. Chaos 25 1550188
[16]	Sam I S, Devaraj P and Bhuvaneswaran R S 2012 Multimed Tools Appl. 56 315
[17]	Zhang G and Liu Q 2011 Opt. Commun. 284 2775
[18]	Wang X and He G 2011 Opt. Commun. 284 5804
[19]	Eslami Z and Bakhshandeh A 2013 Opt. Commun. 286 51
[20]	Akhavan A, Samsudin A and Akhshani A 2015 Opt. Commun. 350 77
[21]	Wang X Y and Liu L T 2013 Nonlinear Dyn. 73 795
[22]	Mirzaei O, Yaghoobi M and Irani H 2012 Nonlinear Dyn. 67 557
[23]	Li C Q, Liu Y S, Xie T and Chen Michael Z Q 2013 Nonlinear Dyn. 73 2083
[24]	Zhu C 2012 Opt. Commun. 285 29
[25]	Xie Eric Y, Li C Q, Yu S M and Lü J H 2017 Signal Process. 132 150
[26]	Shannon C E 1949 Bell Syst. Tech. J. 28 656
[27]	Wang X Y, Liu C M, Xu D H and Liu C X 2016 Nonlinear Dyn. 84 1417
[28]	Ye G D and Huang X L 2016 Secur. Commun. Netw. 9 2015
[29]	Yao W, Zhang X, Zheng Z M and Qiu W J 2015 Nonlinear Dyn. 81 151
[30]	Xu L, Li Z, Li J and Hua W 2016 Opt. Lasers Eng. 78 17
[31]	Liu H J and Wang X Y 2011 Opt. Commun. 284 3895
[32]	Zhou Y C, Cao W J and Philip Chen C L 2014 Signal Process. 100 197
[33]	Safwan EI Assad and Mousa Farajallah 2016 Signal Process. Image Commun. 41 144
[34]	Zhu Z L, Zhang W, Wong K W and Yu H 2011 Inform. Sci. 181 1171
[35]	Liu H J and Wang X Y 2011 Opt. Commun. 284 3895
[36]	Martin Del Rey A and Rodriguez Sanchez G 2015 Int. J. Mod. Phys. C 26 1450069
[37]	Hua Z Y and Zhou Y C 2016 Inform. Sci. 339 237
[38]	Zhang Y S and Xiao D 2014 Commun. Nonlinear Sci. Numer. Simul. 19 74
[39]	Zhang W, Wong K, Yu H and Zhu Z L 2013 Commun. Nonlinear Sci. Numer. Simul. 18 584
[40]	Fu C, Meng W H, Zhan Y F, Zhu Z L, Francis C M Lau, Chi K Tse and Ma H F 2013 Comput. Biol. Med. 43 1000
[41]	Wang X Y and Zhang H L 2015 Opt. Commun. 342 51
[42]	Chua L O 1971 IEEE Trans. Circuit Theory 18 507
[43]	Duan S K, Zhang Y, Hu X, Wang L D and Li C D 2014 Neural Comput. Appl. 25 1437
[44]	Adhikari S P, Yang C, Kim H and Chua L O 2012 IEEE Trans. Neural Netw. Learn. Syst. 23 1426
[45]	Theesar S J S and Balasubramaniam P 2014 Circuits Syst. Signal Process. 33 37
[46]	Li Y X, Huang X and Song Y W 2015 Int. J. Bifur. Chaos 25 1550151
[47]	Zhou Y C, Bao L and Philip Chen C L 2014 Signal Process. 97 172
[48]	Àlvarez G and Li S 2006 Int. J. Bifur. Chaos 16 2129
[49]	Mirzaei O, Yaghoobi M and Irani H 2012 Nonlinear Dyn. 67 557
[50]	Wang X Y and Xu D H 2014 Nonlinear Dyn. 75 345
[51]	Hsiao Hung-I and Lee Junghsi 2015 Signal Process. 117 281
[52]	Liu H, Wang X and Kadir A 2012 Appl. Soft Comput. 12 1457

[1]	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.
[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]	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.
[4]	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.
[5]	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.
[6]	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.
[7]	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.
[8]	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.
[9]	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.
[10]	Fractal sorting vector-based least significant bit chaotic permutation for image encryption Yong-Jin Xian(咸永锦), Xing-Yuan Wang(王兴元), Ying-Qian Zhang(张盈谦), Xiao-Yu Wang(王晓雨), and Xiao-Hui Du(杜晓慧). Chin. Phys. B, 2021, 30(6): 060508.
[11]	An image encryption algorithm based on improved baker transformation and chaotic S-box Xing-Yuan Wang(王兴元), Huai-Huai Sun(孙怀怀), and Hao Gao(高浩). Chin. Phys. B, 2021, 30(6): 060507.
[12]	Ghost imaging-based optical cryptosystem for multiple images using integral property of the Fourier transform Yi Kang(康祎), Leihong Zhang(张雷洪), Hualong Ye(叶华龙), Dawei Zhang(张大伟), and Songlin Zhuang(庄松林). Chin. Phys. B, 2021, 30(12): 124207.
[13]	A secure image protection algorithm by steganography and encryption using the 2D-TSCC Qi Li(李琦), Xingyuan Wang(王兴元), He Wang(王赫), Xiaolin Ye(叶晓林), Shuang Zhou(周双), Suo Gao(高锁), and Yunqing Shi(施云庆). Chin. Phys. B, 2021, 30(11): 110501.
[14]	Memristor-based hyper-chaotic circuit for image encryption 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). Chin. Phys. B, 2020, 29(11): 110504.
[15]	Phase retrieval algorithm for optical information security Shi-Qing Wang(王诗晴), Xiang-Feng Meng(孟祥锋), Yu-Rong Wang(王玉荣), Yong-Kai Yin(殷永凯), Xiu-Lun Yang(杨修伦). Chin. Phys. B, 2019, 28(8): 084203.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

An image encryption scheme based on three-dimensional Brownian motion and chaotic system

Cite this article:

Online attention