Nonlinear Dynamics

, Volume 83, Issue 4, pp 2067–2077 | Cite as

Chaotic image encryption algorithm using wave-line permutation and block diffusion

Original Paper


An efficient and secure image encryption algorithm is proposed in this manuscript using SHA-3 hash function together with double two-dimensional Arnold chaotic maps. Classical encryption architecture, i.e., permutation plus diffusion, is employed in our scheme. To avoid time consumption of sorting operation for pixel position index in permutation stage, a novel wave-line-based confusion is suggested with four random directions of shuffling. The keystream generated by Arnold map is used for vertical and horizontal circular confusions, respectively, in which the initial conditions are updated by the SHA-3 hash values of chaotic matrix and a new vector produced from the plain-image. As a result, the proposed scheme can resist the known-plaintext attack compared with some existing encryption methods. Furthermore, in diffusion stage, a blocking method is designed with the outputs of hash values in the former block permuted image which are used to update again the initial conditions for Arnold map. The current block will influence the next block during the iterations, of which can resist well the chosen-plaintext attack. Numerical results show that the proposed encryption algorithm can have higher security and faster implementation for digital image communication.


Image encryption SHA-3 Arnold map Wave-line  Block 



The authors would like to thank the three anonymous reviewers for valuable comments which are very useful in improving the quality of this manuscript. The work described in this paper was fully supported by the National Natural Science Foundation of China (No. 11301091), the Natural Science Foundation of Guangdong Province of China (No. 2015A030313614), the Project of Enhancing School With Innovation of Guangdong Ocean University of China (No. Q14217), and the Science & Technology Planning Project of Zhanjiang City of China (Nos. 2015B01051, 2015B01098).


  1. 1.
    Matthews, R.: On the derivation of a chaotic encryption algorithm. Cryptologia 13, 29–42 (1989)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Wong, K.W., Kwok, B.S.H., Law, W.S.: A fast image encryption scheme based on chaotic standard map. Phys. Lett. A 372, 2645–2652 (2008)CrossRefMATHGoogle Scholar
  3. 3.
    Cheng, H., Li, X.B.: Partial encryption of compressed image and videos. IEEE Trans. Signal Process. 48, 2439–2451 (2000)CrossRefGoogle Scholar
  4. 4.
    Hua, Z.Y., Zhou, Y.C., Pun, C.M., Chen, C.L.P.: 2D Sine Logistic modulation map for image encryption. Inf. Sci. 297, 80–94 (2015)CrossRefGoogle Scholar
  5. 5.
    Hammami, S.: State feedback-based secure image cryptosystem using hyperchaotic synchronization. ISA Trans. 54, 52–59 (2015)CrossRefGoogle Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    Amin, M., Faragallah, O.S., El-Latif, A.A.A.: A chaotic block cipher algorithm for image cryptosystems. Commun. Nonlinear Sci. Numer. Simul. 15, 3484–3497 (2010)CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    Zhou, Y.C., Bao, L., Chen, C.L.P.: Image encryption using a new parametric switching chaotic system. Signal Process. 93, 3039–3052 (2013)CrossRefGoogle Scholar
  9. 9.
    Norouzi, B., Seyedzadeh, S.M., Mirzakuchaki, S., Mosavi, M.R.: A novel image encryption based on hash function with only two-round diffusion process. Multimed. Syst. 20, 45–64 (2014)CrossRefGoogle Scholar
  10. 10.
    Liu, G.Y., Li, J., Liu, H.J.: Chaos-based color pathological image encryption scheme using one-time keys. Comput. Biol. Med. 45, 111–117 (2014)CrossRefGoogle Scholar
  11. 11.
    Fouda, J.S.A.E., Effa, J.Y., Sabat, S.L., Ali, M.: A fast chaotic block cipher for image encryption. Commun. Nonlinear Sci. Numer. Simul. 9, 578–588 (2014)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Sen Teh, J., Samsudin, A., Akhavan, A.: Parallel chaotic hash function based on the shuffle-exchange network. Nonlinear Dyn. 81, 1067–1079 (2015)CrossRefGoogle Scholar
  13. 13.
    Özkaynak, F., Özer, A.B., Yavuz, S.: Cryptanalysis of a novel image encryption scheme based on improved hyperchaotic sequences. Opt. Commun. 285, 4946–4948 (2012)CrossRefGoogle Scholar
  14. 14.
    Zhu, C.X.: A novel image encryption scheme based on improved hyperchaotic sequences. Opt. Commun. 285, 29–37 (2012)CrossRefGoogle Scholar
  15. 15.
    Wang, X.Y., Liu, L.T.: Cryptanalysis of a parallel sub-image encryption method with high-dimensional chaos. Nonlinear Dyn. 73, 795–800 (2013)CrossRefMATHGoogle Scholar
  16. 16.
    Mirzaei, O., Yaghoobi, M., Irani, H.: A new image encryption method: parallel sub-image encryption with hyper chaos. Nonlinear Dyn. 67, 557–566 (2012)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Solak, E., Çokal, C., Yildiz, O.T., Biyikiǧlu, T.: Cryptoanalysis of Fridrich’s chaotic image encryption. Int. J. Bifurcat. Chaos. 20, 1405–1413 (2010)CrossRefMATHGoogle Scholar
  18. 18.
    Farajallah, M., Fawaz, Z., El Assad, S., Déforges, O.: Efficient image encryption and authentication scheme based on chaotic sequences. In: The 7th International Conference on Emerging Security Information, Systems and Technologies, pp.150–155 (2013)Google Scholar
  19. 19.
    Luo, Y.L., Du, M.H., Liu, J.X.: A symmetrical image encryption scheme in wavelet and time domain. Commun. Nonlinear Sci. Numer. Simul. 20, 447–460 (2015)CrossRefGoogle Scholar
  20. 20.
    Ye, R.S.: A novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism. Opt. Commun. 284, 5290–5298 (2011)CrossRefGoogle Scholar
  21. 21.
    Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: The Keccak sponge function family.
  22. 22.
    Ye, G.D., Wong, K.W.: An efficient chaotic image encryption algorithm based on a generalized Arnold map. Nonlinear Dyn. 69, 2079– 2087 (2012)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Deng, S.J., Zhan, Y.P., Xiao, D., Li, Y.T.: Analysis and improvement of a hash-based image encryption algorithm. Commun. Nonlinear Sci. Numer. Simul. 16, 3269–3278 (2011)CrossRefMathSciNetGoogle Scholar
  24. 24.
    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)CrossRefMATHGoogle Scholar
  25. 25.
    Alvarez, G., Li, S.J.: Some basic cryptographic requirements for chaos based cryptosystems. Int. J. Bifurcat. Chaos. 16, 2129–2151 (2006)CrossRefMathSciNetMATHGoogle Scholar
  26. 26.
    Murillo-Escobar, M.A., Cruz-Hernández, C., Abundiz-Pérez, F., López-Gutiérrez, R.M., Acosta Del Campo, O.R.: A RGB image encryption algorithm based on total plain image characteristics and chaos. Signal Process. 109, 119–131 (2015)CrossRefGoogle Scholar
  27. 27.
    Eslami, Z., Bakhshandeh, A.: An improvement over an image encryption method based on total shuffling. Opt. Commun. 286, 51–55 (2013)CrossRefGoogle Scholar
  28. 28.
    Pareschi, F., Rovatti, R., Setti, G.: On statistical tests for randomness included in the NIST SP800-22 test suite and based on the binomial distribution. IEEE Trans. Inf. Forensics Secur. 7, 491–505 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.College of ScienceGuangdong Ocean UniversityZhanjiangChina
  2. 2.School of Mathematics and Computation ScienceLingnan Normal UniversityZhanjiangChina

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