Design of an image encryption scheme based on a multiple chaotic map

Abstract In order to solve the problem that chaos is degenerated in limited computer precision and Cat map is the small key space, this paper presents a chaotic map based on topological conjugacy and the chaotic characteristics are proved by Devaney definition. In order to produce a large key space, a Cat map named block Cat map is also designed for permutation process based on multiple-dimensional chaotic maps. The image encryption algorithm is based on permutation–substitution, and each key is controlled by different chaotic maps. The entropy analysis, differential analysis, weak-keys analysis, statistical analysis, cipher random analysis, and cipher sensibility analysis depending on key and plaintext are introduced to test the security of the new image encryption scheme. Through the comparison to the proposed scheme with AES, DES and Logistic encryption methods, we come to the conclusion that the image encryption method solves the problem of low precision of one dimensional chaotic function and has higher speed and higher security.

[1]  Nikolaos G. Bourbakis,et al.  Picture data encryption using scan patterns , 1992, Pattern Recognit..

[2]  Jinsheng Sun,et al.  A block cipher based on a suitable use of the chaotic standard map , 2005 .

[3]  W. Tang,et al.  A fast image encryption system based on chaotic maps with finite precision representation , 2007 .

[4]  K. Aihara,et al.  Cryptosystems with discretized chaotic maps , 2002 .

[5]  Olcay Taner Yildiz,et al.  Cryptanalysis of Fridrich's Chaotic Image Encryption , 2010, Int. J. Bifurc. Chaos.

[6]  Yong Wang,et al.  A new chaos-based fast image encryption algorithm , 2011, Appl. Soft Comput..

[7]  Qing Zhou,et al.  A novel image encryption algorithm based on self-adaptive wave transmission , 2010, Signal Process..

[8]  Guanrong Chen,et al.  On the security defects of an image encryption scheme , 2009, Image Vis. Comput..

[9]  Xiaojun Tong,et al.  Image encryption scheme based on 3D baker with dynamical compound chaotic sequence cipher generator , 2009, Signal Process..

[10]  Di Xiao,et al.  Analysis and improvement of a chaos-based image encryption algorithm , 2009 .

[11]  Vinod Patidar,et al.  Image encryption using chaotic logistic map , 2006, Image Vis. Comput..

[12]  J. Fridrich.  Symmetric Ciphers Based on Two-Dimensional Chaotic Maps , 1998 .

[13]  Shujun Li,et al.  Breaking a modified substitution-diffusion image cipher based on chaotic standard and logistic maps , 2009, ArXiv.

[14]  A. Akhavan,et al.  A novel algorithm for image encryption based on mixture of chaotic maps , 2008 .

[15]  Nikolaos G. Bourbakis,et al.  A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks , 2008, Signal Process. Image Commun..

[16]  Kwok-Wo Wong,et al.  A fast image encryption and authentication scheme based on chaotic maps , 2010 .

[17]  Amir Akhavan,et al.  A novel scheme for image encryption based on 2D piecewise chaotic maps , 2010 .