Skip to main content
SpringerLink
Log in

Cryptanalysis of a chaotic image cipher using Latin square-based confusion and diffusion

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

Abstract

Recently, an interesting variant of chaotic image cipher using Latin square has been studied extensively, but the lack of the corresponding cryptanalysis hampers its further development. This paper performs the cryptanalysis of a newly proposed chaotic image cipher using Latin square-based confusion and diffusion. Despite the claim that the cryptosystem is of high security, we demonstrate that the cipher can be broken by chosen-plaintext attack combined with chosen-ciphertext attack. Moreover, some improvement ideas for the original algorithm are given to enhance the security.

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. Ahmad, M., Ahmad, F.: Cryptanalysis of image encryption based on permutation-substitution using chaotic map and Latin square image cipher. In: Proceedings of the 3rd international conference on Frontiers of intelligent computing: theory and applications (FICTA) 2014, pp. 481–488. Springer (2015)

  2. Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurcat. Chaos 16(08), 2129–2151 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Alvarez, G., Montoya, P., Pastor, G., Romera, M.: Chaotic cryptosystems. In: Proceedings of the IEEE 33rd annual international Carnahan conference on security technology, pp. 332–338. IEEE (1999)

  4. Chapaneri, S., Chapaneri, R.: Chaos based image encryption using latin rectangle scrambling. In: 2014 annual IEEE India conference (INDICON), pp. 1–6. IEEE (2014)

  5. Chen, G., Mao, Y., Chui, C.K.: A symmetric image encryption scheme based on 3d chaotic cat maps. Chaos Solitons Fractals 21(3), 749–761 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, J.X., Zhu, Z.L., Fu, C., Yu, H.: A fast image encryption scheme with a novel pixel swapping-based confusion approach. Nonlinear Dynamics 77(4), 1191–1207 (2014)

    Article  Google Scholar 

  7. Chen, J.X., Zhu, Z.L., Fu, C., Yu, H., Zhang, L.B.: An efficient image encryption scheme using gray code based permutation approach. Opt. Lasers Eng. 67, 191–204 (2015)

    Article  Google Scholar 

  8. Chen, J.X., Zhu, Z.L., Fu, C., Zhang, L.B., Zhang, Y.: An efficient image encryption scheme using lookup table-based confusion and diffusion. Nonlinear Dynamics 81(3), 1151–1166 (2015)

    Article  Google Scholar 

  9. Diaconu, A.V.: An image encryption algorithm with a chaotic dynamical system based sudoku grid. In: 2014 10th international conference on communications (COMM), pp. 1–4. IEEE (2014)

  10. Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps. Int. J. Bifurcat. chaos 8(6), 1259–1284 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  11. Grošek, O., Sỳs, M.: Isotopy of Latin squares in cryptography. Tatra Mt. Math. Publ. 45(1), 27–36 (2010)

    MathSciNet  MATH  Google Scholar 

  12. Gupta, Y., Bansal, A., Baresary, D.: Review on latin square. Int. J. CSMC 3(7), 338–342 (2014)

    Google Scholar 

  13. He, X., Zhu, Q., Gu, P.: A new chaos-based encryption method for color image. Lect. Notes Comput. Sci. 4062, 671–678 (2006)

    Article  MATH  Google Scholar 

  14. Kocarev, L., Jakimoski, G., Stojanovski, T., Parlitz, U.: From chaotic maps to encryption schemes. In: Proceedings of the 1998 IEEE international symposium on circuits and systems, vol. 4, pp. 514–517. IEEE (1998)

  15. Kong, J.: The role of latin square in cipher systems: matrix approach to model encryption modes of operation. UCLA Computer Science Department Technical Report CSTR030038 (2008)

  16. Kumar, S.N., Kumar, H.S., Panduranga, H.: Hardware software co-simulation of dual image encryption using latin square image. In: 2013 fourth international conference on computing, communications and networking technologies (ICCCNT), pp. 1–5. IEEE (2013)

  17. Li, C.: Cracking a hierarchical chaotic image encryption algorithm based on permutation. Signal Process. 118, 203–210 (2016)

    Article  Google Scholar 

  18. Li, C., Chen, G.: On the security of a class of image encryption schemes. In: Proceeding of IEEE international symposium on circuits and systems, pp. 3290–3293. IEEE (2008)

  19. Li, C., Liu, Y., Xie, T., Chen, M.Z.: Breaking a novel image encryption scheme based on improved hyperchaotic sequences. Nonlinear Dynamics 73(3), 2083–2089 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  20. Li, C., Lo, K.T.: Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal Process. 91(4), 949–954 (2011)

    Article  MATH  Google Scholar 

  21. Machkour, M., Saaidi, A., Benmaati, M.: A novel image encryption algorithm based on the two-dimensional logistic map and the latin square image cipher. 3D Research 6(4), 1–18 (2015)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  23. Pal, S.K., Kapoor, S., Arora, A., Chaudhary, R., Khurana, J.: Design of strong cryptographic schemes based on latin squares. J. Discrete Math. Sci. Cryptogr. 13(3), 233–256 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  24. Panduranga, H., Kumar, S.N., et al.: Image encryption based on permutation-substitution using chaotic map and latin square image cipher. Eur. Phys. J. Spec. Top. 223(8), 1663–1677 (2014)

    Article  Google Scholar 

  25. Shen, J., Jin, X., Zhou, C.: A color image encryption algorithm based on magic cube transformation and modular arithmetic operation. Lect. Notes Comput. Sci. 3768, 270–280 (2005)

    Article  Google Scholar 

  26. Solak, E., Çokal, C., Yildiz, O.T., Biyikoglu, T.: Cryptanalysis of Fridrich’s chaotic image encryption. Int. J. Bifurcat. Chaos 20(5), 1405–1413 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  27. Stinson, D.R.: Cryptography: Theory and Practice. CRC press, Boca Raton (2005)

    MATH  Google Scholar 

  28. Williams Jr, L.F.: A modification to the half-interval search (binary search) method. In: Proceedings of the 14th annual Southeast regional conference, pp. 95–101. ACM (1976)

  29. Wu, Y., Noonan, J.P., Agaian, S.: Dynamic and implicit latin square doubly stochastic s-boxes with reversibility. In: 2011 IEEE international conference on systems, man and cybernetics (SMC), pp. 3358–3364. IEEE (2011)

  30. Wu, Y., Zhou, Y., Noonan, J.P., Agaian, S.: Design of image cipher using latin squares. Inf. Sci. 264(20), 317–339 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  31. Xie, E.Y., Li, C., Yu, S., Lü, J.: On the cryptanalysis of Fridrich’s chaotic image encryption scheme. Signal Process. 132, 150–154 (2017)

    Article  Google Scholar 

  32. Yap, W.S., Phan, R.C.W., Goi, B.M., Yau, W.C., Heng, S.H.: On the effective subkey space of some image encryption algorithms using external key. J. Vis. Commun. Image Represent. 40, 51–57 (2016)

  33. Yeo, J.C., Guo, J.I.: Efficient hierarchical chaotic image encryption algorithm and its vlsi realisation. IEE Proc. Vis. Image Signal process. 147(2), 167–175 (2000)

    Article  Google Scholar 

  34. Zhang, X., Zhao, Z.: Chaos-based image encryption with total shuffling and bidirectional diffusion. Nonlinear Dynamics 75(1), 319–330 (2014)

    Article  MathSciNet  Google Scholar 

  35. Zhu, C.: A novel image encryption scheme based on improved hyperchaotic sequences. Opt. Commun. 285(1), 29–37 (2012)

    Article  Google Scholar 

Download references

Acknowledgements

The work was funded by the National Natural Science Foundation of China (Grant Nos. 61472464, 61502399, 61572089, 61633005), the Chongqing Higher Education Reform Projects (Grant No. 153012), the Chongqing Graduate Student Research Innovation Projects (Grant No. CYB14002), the Fundamental Research Funds for the Central Universities (Grant No. 106112014CDJZR185501) and the Research Program of Chongqing Education Commission (Grant No. JK15012027).

Author information

Authors and Affiliations

  1. Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, College of Computer Science, Chongqing University, Chongqing, 400044, China

    Guiqiang Hu, Di Xiao & Xinyan Li

  2. Key Laboratory of Electronic Commerce and Logistics of Chongqing, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Yong Wang

  3. School of Mathematics and Statistics, Yangtze Normal University, Chongqing, 408100, China

    Xinyan Li

Authors
  1. Guiqiang Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Di Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xinyan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Di Xiao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, G., Xiao, D., Wang, Y. et al. Cryptanalysis of a chaotic image cipher using Latin square-based confusion and diffusion. Nonlinear Dyn 88, 1305–1316 (2017). https://doi.org/10.1007/s11071-016-3311-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-3311-2

Keywords

Search

Navigation