Skip to main content
SpringerLink
Log in

An efficient chaotic image encryption algorithm based on a generalized Arnold map

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

An efficient image encryption algorithm using the generalized Arnold map is proposed. The algorithm is composed of two stages, i.e., permutation and diffusion. First, a total circular function, rather than the traditional periodic position permutation, is used in the permutation stage. It can substantially reduce the correlation between adjacent pixels. Then, in the stage of diffusion, double diffusion functions, i.e., positive and opposite module, are utilized with a novel generation of the keystream. As the keystream depends on the processed image, the proposed method can resist known- and chosen-plaintext attacks. Experimental results and theoretical analysis indicate the effectiveness of our method. An extension of the proposed algorithm to other chaotic systems is also discussed.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Dang, P.P., Chau, P.M.: Image encryption for secure internet multimedia applications. IEEE Trans. Consum. Electron. 46, 395–403 (2000)

    Article  Google Scholar 

  2. Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps. Int. J. Bifurc. Chaos 8, 1259–1284 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hennelly, B.M., Sheridan, J.T.: Image encryption and the fractional Fourier transform. Optik 114, 251–265 (2003)

    Article  Google Scholar 

  4. Liao, X.F., Lai, S.Y., Zhou, Q.: A novel image encryption algorithm based on self-adaptive wave transmission. Signal Process. 90, 2714–2722 (2010)

    Article  MATH  Google Scholar 

  5. Wang, Y., Wong, K.W., Liao, X.F., Chen, G.R.: A new chaos-based fast image encryption algorithm. Appl. Soft Comput. 11, 514–522 (2011)

    Article  Google Scholar 

  6. Gao, T.G., Chen, Z.Q.: Image encryption based on a new total shuffling algorithm. Chaos Solitons Fractals 38, 213–220 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mazloom, S., Eftekhari-Moghadam, A.M.: Color image encryption based on coupled nonlinear chaotic map. Chaos Solitons Fractals 42, 1745–1754 (2009)

    Article  MATH  Google Scholar 

  8. Gao, H.J., Zhang, Y.S., Liang, S.Y., Li, D.Q.: A new chaotic algorithm for image encryption. Chaos Solitons Fractals 29, 393–399 (2005)

    Article  Google Scholar 

  9. Patidar, V., Pareek, N.K., Purohit, G., Sud, K.K.: A robust and secure chaotic standard map based pseudorandom permutation-substitution scheme for image encryption. Opt. Commun. 284, 4331–4339 (2011)

    Article  Google Scholar 

  10. Mao, Y.B., Chen, G.R., Lian, S.G.: A novel fast image encryption scheme based on 3D chaotic baker maps. Int. J. Bifurc. Chaos 14, 3613–3624 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Banerjee, S., Ghosh, D., Ray, A., Chowdhury, A.R.: Synchronization between two different time-delayed systems and image encryption. Europhys. Lett. 81, 20006 (2008). doi:10.1209/0295-5075/81/20006

    Article  Google Scholar 

  12. Ghosh, D., Banerjee, S., Chowdhury, A.R.: Synchronization between variable time-delayed systems and cryptography. Europhys. Lett. 80, 30006 (2007). doi:10.1209/0295-5075/80/30006

    Article  MathSciNet  Google Scholar 

  13. Alvarez, G., Li, S.J.: Cryptanalyzing a nonlinear chaotic algorithm (NCA) for image encryption. Commun. Nonlinear Sci. Numer. Simul. 14, 3743–3749 (2009)

    Article  Google Scholar 

  14. Cokal, C., Solak, E.: Cryptanalysis of a chaos-based image encryption algorithm. Phys. Lett. A 373, 1357–1360 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Guan, Z.H., Huang, F.J., Guan, W.J.: Chaos-based image encryption algorithm. Phys. Lett. A 346, 153–157 (2005)

    Article  MATH  Google Scholar 

  16. Ye, R.S.: A novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism. Opt. Commun. 284, 5290–5298 (2011)

    Article  Google Scholar 

  17. Wong, K.W., Kwok, B.S.H., Yuen, C.H.: An efficient diffusion approach for chaos-based image encryption. Chaos Solitons Fractals 41, 2652–2663 (2009)

    Article  MATH  Google Scholar 

  18. Huang, X.L.: Image encryption algorithm using chaotic Chebyshev generator. Nonlinear Dyn. 67, 2411–2417 (2012)

    Article  Google Scholar 

Download references

Acknowledgements

This work is part of the research project funded by the Science & Technology Program Foundation of Zhanjiang City of P.R. China (No. 2010C3112007). The authors would like to thank the editor and the anonymous reviewers for the useful comments and suggestions given.

Author information

Authors and Affiliations

  1. College of Science, Guangdong Ocean University, Zhanjiang, 524088, Guangdong, P.R. China

    Guodong Ye

  2. Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, P.R. China

    Guodong Ye & Kwok-Wo Wong

Authors
  1. Guodong Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kwok-Wo Wong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guodong Ye.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ye, G., Wong, KW. An efficient chaotic image encryption algorithm based on a generalized Arnold map. Nonlinear Dyn 69, 2079–2087 (2012). https://doi.org/10.1007/s11071-012-0409-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-012-0409-z

Keywords

Search

Navigation