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Chin. Phys. B, 2017, Vol. 26(2): 020504    DOI: 10.1088/1674-1056/26/2/020504
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An image encryption scheme based on three-dimensional Brownian motion and chaotic system

Xiu-Li Chai(柴秀丽)1,2, Zhi-Hua Gan(甘志华)3, Ke Yuan(袁科)1, Yang Lu(路杨)4, Yi-Ran Chen(陈怡然)2
1 School of Computer and Information Engineering, Institute of Image Processing and Pattern Recognition, Henan University, Kaifeng 475004, China;
2 Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA;
3 School of Software, Henan University, Kaifeng 475004, China;
4 Research Department, Henan University, Kaifeng 475004, China
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:

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

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