Abstract
In this paper, we introduce a new image encryption scheme based on fractional chaotic time series, in which shuffling the positions blocks of plain-image and changing the grey values of image pixels are combined to confuse the relationship between the plain-image and the cipher-image. Also, the experimental results demonstrate that the key space is large enough to resist the brute-force attack and the distribution of grey values of the encrypted image has a random-like behavior.
References
[1] M.S. Baptista, Cryptography with chaos. Physics Letters A, 1998; 240: 50–54. 10.1016/S0375-9601(98)00086-3Search in Google Scholar
[2] H.K.C. Chang, J.L. Liu, A linear quadtree compression scheme for image encryption. Signal Process Image Commun. 1997; 10: 279–90. 10.1016/S0923-5965(96)00025-2Search in Google Scholar
[3] C.C. Chang, M.S. Hwang, T.S. Chen, A new encryption alogorithm for image cryptosystems. J. Syst. Softw. 2001; 58: 83-91. Search in Google Scholar
[4] J. Daemen, B. Sand, V. Rijmen, The Design of Rijndael: AES–The Advanced Encryption Standard. Springer-Verlag, Berlin, 2002. 10.1007/978-3-662-04722-4_1Search in Google Scholar
[5] X.L. Huang, Image encryption algorithm using chaotic chebyshev generator. Nonlinear. Dyn. 2012; 64: 2411–2417. Search in Google Scholar
[6] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. in: North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V, Amsterdam, 2006. Search in Google Scholar
[7] L. Kocarev, Chaos-based cryptography: a brief overview. IEEE Circ. Syst. Mag. 2001; 1: 6–21. Search in Google Scholar
[8] S. Lian, J. Sun, Z. Wang, A block cipher based on a suitable use of the chaotic standard map. Chaos, Solitons and Fractals, 2005; 26: 117–29. 10.1016/j.chaos.2004.11.096Search in Google Scholar
[9] A.N. Pisarchik, M. Zanin, Image encryption with chaotically coupled chaotic maps. Physica D, 2008; 237: 2638–2648. 10.1016/j.physd.2008.03.049Search in Google Scholar
[10] R. Rhouma, S. Meherzi, S. Belghith, OCML-based colour image encryption. Chaos, Solitons and Fractals, 2009; 40: 309–318. 10.1016/j.chaos.2007.07.083Search in Google Scholar
[11] J. Scharinger, Fast encryption of image data using chaotic Kolmogorov flows. J Electron Imaging, 1998; 7: 318–25. 10.1117/1.482647Search in Google Scholar
[12] B. Schneier, Applied Cryptography–Protocols, Algorithms, and Source Code. second ed., C. John Wiley and Sons, Inc., New York, 1996. Search in Google Scholar
[13] V.V. Uchaikin, Fractional Derivatives for Physicists and Engineers. Springer, New York, 2012. 10.1007/978-3-642-33911-0Search in Google Scholar
[14] X.Y. Wang, C.H. Yu, Cryptanalysis and improvement on a cryptosystem based on a chaotic map. Computers and Mathematics with Applications, 2009; 57: 476–482. 10.1016/j.camwa.2008.09.042Search in Google Scholar
[15] J. Wei, X. Liao, K.W. Wong, T. Zhou, Cryptanalysis of a cryptosystem using multiple one-dimensional chaotic maps. Commun Nonlinear Sci Numer Simul. 2007; 12: 814–22. 10.1016/j.cnsns.2005.06.001Search in Google Scholar
[16] C.G. Li, G.R. Chen, Chaos and hyperchaos in the fractional-order Rossler equations. Physica A-Statistical Mechanics and Its Applications, 2004; 341: 55–61. 10.1016/j.physa.2004.04.113Search in Google Scholar
[17] C.G. Li, G.R. Chen, Chaos in the fractional order Chen system and its control. Chaos Solitons Fractals, 2004; 22: 549–554. 10.1016/j.chaos.2004.02.035Search in Google Scholar
[18] Y. Zhou, F. Jiao, Existence of mild solutions for fractional neutral evolution equations. Comput. Math. Appl. 2010; 59: 1063–1077. Search in Google Scholar
[19] Y. Zhou, F. Jiao, Nonlocal Cauchy problem for fractional evolution equations. Nonlinear Anal. 2010; 11: 4465–4475. 10.1016/j.nonrwa.2010.05.029Search in Google Scholar
©2015 Guo et al.
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
