Abstract
In recent years, the chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. In this paper, permutation and substitution methods are incorporated to present a stronger image encryption algorithm. Spatial chaotic maps are used to realize the position permutation, and to confuse the relationship between the cipher-image and the plain-image. The experimental results demonstrate that the suggested encryption scheme of image has the advantages of large key space and high security; moreover, the distribution of grey values of the encrypted image has a random-like behavior.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Hao B L. Starting with Parabolas: An Introduction to Chaotic Dynamics. Shanghai: Shanghai Scientific and Technological Education Publishing House, 1993
Brown R, Chua L O. Clarifying chaos: Examples and counterexamples. Int J Bifurcat Chaos, 1996, 6(2): 219–242[DOI]
Lasota A, Mackey M C. Chaos, Fractals, and Noise Stochastic Aspects of Dynamics. 2nd ed. New York: Springer, 1994
Yan S L, Chi Y Y, Chen W J. Chaotic laser synchronization and its application in optical fiber secure communication. Sci China Ser F-Inf Sci, 2004, 47(3): 332–347[DOI]
Dai J H. Chaotic application in information encryption. Chin Sci Bull, 1996, 41(5): 402–405
Zhang Y, Yu J M, Du G H. Continuous feedback chaotic synchronization and its application in secure communication. Chin Sci Bull, 1998, 43(17): 1831–1835
Zhou C S, Lai C H. Extracting messages masked by chaotic signals of time-delay systems. Phys Rev E, 1999, 60: 320–323[DOI]
Chang H K C, Liu J L. A linear quadtree compression scheme for image encryption. Signal Process-Image Commun, 1997, 10(4): 279–290[DOI]
Lu H P, Wang S H, Li X W, et al. A new spatiotemporally chaotic cryptosystem and its security and performance analyses. Chaos, 2004, 14(3): 617–629[DOI]
Yen J C, Guo J I. A new chaotic key-based design for image encryption and decryption. In: Proc IEEE Int Symposium on Circuits and Systems. Geneva: IEEE, 2000, 4: 49–52
Chen G R, Mao Y B, Chui C K. A symmetric image encryption scheme based on 3D chaotic cat maps. Int J Bifurcat Chaos Solitons Fractals, 2004, 21: 749–761[DOI]
Pareek N K, Patidar V, Sud K K. Cryptography using multiple one-dimensional chaotic maps. Commun Nonlinear Sci Number Simul, 2005, 10(7): 715–723[DOI]
Garcia P, Parravano A, Cosenza M G, et al. Coupled map networks as communication schemes. Phys Rev E, 2002, 65: 045201[DOI]
Zhou H, Ling X T. Problems with the chaotic inverse system encryption approach. IEEE Trans Circ Syst I, 1997, 44(3): 268–271[DOI]
Pareek N K, Patidar V, Sud K K. Image encryption using chaotic logistic map. Image Vision Comput, 2006, 24(9): 926–934[DOI]
Li P, Li Z, Halang W A, et al. A multiple pseudorandom-bit generator based on a spatiotemporal chaotic map. Phys Lett A, 2006, 349: 467–473[DOI]
Wang S H, Liu W R, Lu H P, et al. Periodicity of chaotic trajectories of single and coupled maps in realizations of finite computer precisions. Int J Mod Phys B, 2004, 18(17–19): 2617–2622[DOI]
Parker A T, Short K M. Reconstructing the keystream from a chaotic encryption scheme. IEEE Trans Circuits Syst I, 2001, 48(5): 104–112
Wang K, Pei W J, Zou L H, et al. Security of public key encryption technique based on multiple chaotic systems. Phys Lett A, 2006, 360: 259–262[DOI]
Kaneko K, Tsuda I. Complex Systems: Chaos and Beyond. Tokyo: Asakura, 1996
Yang W M. On the largest exponent for coupled surjective map lattice with weak diffusive coupling. Chaos Solitons Fractals, 1991, 1: 389–396[DOI]
Liu S T, Wu S. Uniformity of spatial physical motion systems and spatial chaos behavior in the sense of Li-Yorke. Int J Bifurcation Chaos Appl Sci Eng, 2006, 16(9): 2697–2703[DOI]
Liu S T, Chen G. On spatial lyapunov exponents and spatial chaos. Int J Bifurcation Chaos Appl Sci Eng, 2003, 13(5): 1163–1181[DOI]
Liu S T, Wu S. Spacial chaos behavior of molecular orbit. Chaos Solitons Fractals, 2007, 31: 1181–1186[DOI]
Liu S T. Nuclear fission and spatial chaos. Chaos Solitons Fractals, 2006, 30: 453–462[DOI]
Liu S T, Chen G. Nonlinear feedback-controlled generalized synchronization of spatial chaos. Chaos Solitons Fractals, 2004, 22(4): 35–46[DOI]
Liu S T, Chen G. Asymptotic behavior of delay 2-D discrete logistic systems. IEEE Trans Circuits Syst I, 2002, 49(11): 1677–1682[DOI]
Chen G, Liu S T. On spatial periodic orbits and spatial chaos. Int J Bifurcation Chaos Appl Sci Eng, 2003, 13(3): 867–876
Chen G, Liu S T. On generalized synchronization of spatial chaos. Chaos Solitons Fractals, 2003, 15(2): 311–318[DOI]
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China (Grant No. 60874009) and the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200444)
Rights and permissions
About this article
Cite this article
Liu, S., Sun, F. Spatial chaos-based image encryption design. Sci. China Ser. G-Phys. Mech. Astron. 52, 177–183 (2009). https://doi.org/10.1007/s11433-009-0032-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11433-009-0032-2