Skip to main content
SpringerLink
Log in

Spatial chaos-based image encryption design

  • Published:
Science in China Series G: Physics, Mechanics and Astronomy Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hao B L. Starting with Parabolas: An Introduction to Chaotic Dynamics. Shanghai: Shanghai Scientific and Technological Education Publishing House, 1993

    Google Scholar 

  2. Brown R, Chua L O. Clarifying chaos: Examples and counterexamples. Int J Bifurcat Chaos, 1996, 6(2): 219–242[DOI]

    Article  MATH  MathSciNet  Google Scholar 

  3. Lasota A, Mackey M C. Chaos, Fractals, and Noise Stochastic Aspects of Dynamics. 2nd ed. New York: Springer, 1994

    MATH  Google Scholar 

  4. 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]

    Article  Google Scholar 

  5. Dai J H. Chaotic application in information encryption. Chin Sci Bull, 1996, 41(5): 402–405

    Google Scholar 

  6. 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

    Article  Google Scholar 

  7. Zhou C S, Lai C H. Extracting messages masked by chaotic signals of time-delay systems. Phys Rev E, 1999, 60: 320–323[DOI]

    Article  ADS  Google Scholar 

  8. 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]

    Article  Google Scholar 

  9. 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]

    Article  ADS  MathSciNet  Google Scholar 

  10. 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

    Google Scholar 

  11. 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]

    Article  MATH  MathSciNet  Google Scholar 

  12. 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]

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. Garcia P, Parravano A, Cosenza M G, et al. Coupled map networks as communication schemes. Phys Rev E, 2002, 65: 045201[DOI]

    Google Scholar 

  14. Zhou H, Ling X T. Problems with the chaotic inverse system encryption approach. IEEE Trans Circ Syst I, 1997, 44(3): 268–271[DOI]

    Article  Google Scholar 

  15. Pareek N K, Patidar V, Sud K K. Image encryption using chaotic logistic map. Image Vision Comput, 2006, 24(9): 926–934[DOI]

    Article  Google Scholar 

  16. 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]

    Article  ADS  Google Scholar 

  17. 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]

    Article  ADS  Google Scholar 

  18. Parker A T, Short K M. Reconstructing the keystream from a chaotic encryption scheme. IEEE Trans Circuits Syst I, 2001, 48(5): 104–112

    Article  MathSciNet  Google Scholar 

  19. 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]

    Article  MATH  ADS  Google Scholar 

  20. Kaneko K, Tsuda I. Complex Systems: Chaos and Beyond. Tokyo: Asakura, 1996

    Google Scholar 

  21. Yang W M. On the largest exponent for coupled surjective map lattice with weak diffusive coupling. Chaos Solitons Fractals, 1991, 1: 389–396[DOI]

    Article  MATH  Google Scholar 

  22. 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]

    Article  MATH  Google Scholar 

  23. 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]

    Article  MATH  Google Scholar 

  24. Liu S T, Wu S. Spacial chaos behavior of molecular orbit. Chaos Solitons Fractals, 2007, 31: 1181–1186[DOI]

    Article  MathSciNet  Google Scholar 

  25. Liu S T. Nuclear fission and spatial chaos. Chaos Solitons Fractals, 2006, 30: 453–462[DOI]

    Article  Google Scholar 

  26. Liu S T, Chen G. Nonlinear feedback-controlled generalized synchronization of spatial chaos. Chaos Solitons Fractals, 2004, 22(4): 35–46[DOI]

    Article  MATH  MathSciNet  Google Scholar 

  27. 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]

    Article  Google Scholar 

  28. Chen G, Liu S T. On spatial periodic orbits and spatial chaos. Int J Bifurcation Chaos Appl Sci Eng, 2003, 13(3): 867–876

    Google Scholar 

  29. Chen G, Liu S T. On generalized synchronization of spatial chaos. Chaos Solitons Fractals, 2003, 15(2): 311–318[DOI]

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Control Science and Engineering, Shandong University, Ji’nan, 250061, China

    ShuTang Liu & FuYan Sun

Authors
  1. ShuTang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. FuYan Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to FuYan Sun.

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

Reprints 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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-009-0032-2

Keywords

Search

Navigation