Double image multi-encryption algorithm based on fractional chaotic time series
Zhenghong Guo ; Jie Yang ; Yang Zhao
Open Mathematics, Tome 13 (2015), / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:276018
@article{bwmeta1.element.doi-10_1515_math-2015-0080,
     author = {Zhenghong Guo and Jie Yang and Yang Zhao},
     title = {Double image multi-encryption algorithm based on fractional chaotic time series},
     journal = {Open Mathematics},
     volume = {13},
     year = {2015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0080}
}
Zhenghong Guo; Jie Yang; Yang Zhao. Double image multi-encryption algorithm based on fractional chaotic time series. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0080/

[1] M.S. Baptista, Cryptography with chaos. Physics Letters A, 1998; 240: 50–54. | Zbl 0936.94013

[2] H.K.C. Chang, J.L. Liu, A linear quadtree compression scheme for image encryption. Signal Process Image Commun. 1997; 10: 279–90. [Crossref]

[3] C.C. Chang, M.S. Hwang, T.S. Chen, A new encryption alogorithm for image cryptosystems. J. Syst. Softw. 2001; 58: 83-91. [Crossref]

[4] J. Daemen, B. Sand, V. Rijmen, The Design of Rijndael: AES–The Advanced Encryption Standard. Springer-Verlag, Berlin, 2002. | Zbl 1065.94005

[5] X.L. Huang, Image encryption algorithm using chaotic chebyshev generator. Nonlinear. Dyn. 2012; 64: 2411–2417. [WoS]

[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. | Zbl 1092.45003

[7] L. Kocarev, Chaos-based cryptography: a brief overview. IEEE Circ. Syst. Mag. 2001; 1: 6–21.

[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. [Crossref] | Zbl 1093.37504

[9] A.N. Pisarchik, M. Zanin, Image encryption with chaotically coupled chaotic maps. Physica D, 2008; 237: 2638–2648. [WoS] | Zbl 1148.94431

[10] R. Rhouma, S. Meherzi, S. Belghith, OCML-based colour image encryption. Chaos, Solitons and Fractals, 2009; 40: 309–318. [WoS][Crossref] | Zbl 1197.94011

[11] J. Scharinger, Fast encryption of image data using chaotic Kolmogorov flows. J Electron Imaging, 1998; 7: 318–25. [Crossref]

[12] B. Schneier, Applied Cryptography–Protocols, Algorithms, and Source Code. second ed., C. John Wiley and Sons, Inc., New York, 1996. | Zbl 0853.94001

[13] V.V. Uchaikin, Fractional Derivatives for Physicists and Engineers. Springer, New York, 2012.

[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. | Zbl 1165.94325

[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. [Crossref][WoS] | Zbl 1169.94337

[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. [WoS]

[17] C.G. Li, G.R. Chen, Chaos in the fractional order Chen system and its control. Chaos Solitons Fractals, 2004; 22: 549–554. [Crossref] | Zbl 1069.37025

[18] Y. Zhou, F. Jiao, Existence of mild solutions for fractional neutral evolution equations. Comput. Math. Appl. 2010; 59: 1063–1077. [Crossref] | Zbl 1189.34154

[19] Y. Zhou, F. Jiao, Nonlocal Cauchy problem for fractional evolution equations. Nonlinear Anal. 2010; 11: 4465–4475. | Zbl 1260.34017