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Algebraic analysis of a RGB image encryption algorithm based on DNA encoding and chaotic map

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Abstract

Recently a new image encryption method based on DNA encoding and chaotic systems has been proposed. In this paper, several weaknesses of this cryptosystem are pointed out. Equivalent mathematical model of the cryptosystem is designed and algebraic analysis is given. Moreover reduction of the key space has been reached by finding equivalent keys. A recovering scheme is finally given with a lower complexity than the actual decryption scheme.

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References

  1. Lian, S.: Multimedia Content Encryption: Techniques and Applications. Taylor & Francis Group, Routledge (2009)

    Google Scholar 

  2. Zhang, H., Liu, D., Wang, Z.: Controlling Chaos: Suppression, Synchronization, and Chaotification. Springer, London (2009)

    Book  Google Scholar 

  3. Shannon, C.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28, 658–715 (1949)

    Google Scholar 

  4. El-Latif, A.A.A., Niu, X.: A hybrid chaotic system and cyclic elliptic curve for image encryption. Int. J. Electron. Commun. 67(2), 136–143 (2012)

    Google Scholar 

  5. Gaoa, T., Chen, Z.: A new image encryption algorithm based on hyper-chaos. Phys. Lett. A 372, 394–400 (2008)

    Article  Google Scholar 

  6. Hermassi, H., Rhouma, R., Belghith, S.: Improvement of an image encryption algorithm based on hyper-chaos. Telecommun. Syst. 52, 539–549 (2013)

    Google Scholar 

  7. Mirzaei, O., Yaghoobi, M., Irani, H.: A new image encryption method: parallel sub-image encryption with hyper chaos. Nonlinear Dyn. 67(1), 557–566 (2012)

    Article  MathSciNet  Google Scholar 

  8. Pareeka, N.K., Patidara, V., Sud, K.K.: Image encryption using chaotic logistic map. Image Vis. Comput. 24(9), 926–934 (2006)

    Article  Google Scholar 

  9. Tang, Zhenjun, Zhang, Xianquan: Secure image encryption without size limitation using Arnold transform and random strategies. J. Multimed. 6(2), 202–206 (2011)

    Google Scholar 

  10. Tong, X.-J., Wang, Z., Zhang, M., Liu, Y.: A new algorithm of the combination of image compression and encryption technology based on cross chaotic map. Nonlinear Dyn. 72(1–2), 229–241 (2013)

    Article  MathSciNet  Google Scholar 

  11. Zhang, X., Zhao, Z.: Chaos-based image encryption with total shuffling and bidirectional diffusion. Nonlinear Dyn. (2013). doi:10.1007/s11071-013-1068-4

  12. Liu, H., Wang, X., Kadir, A.: Image encryption using DNA complementary rule and chaotic maps. Appl. Soft Comput. 12(5), 1457–1466 (2012)

    Article  Google Scholar 

  13. Liu, L., Zhang, Q., Wei, X.: A RGB image encryption algorithm based on DNA encoding and chaos map. Comput. Electr. Eng. 38(5), 1240–1248 (2012)

    Article  Google Scholar 

  14. Wei, X., Guo, L., Zhang, Q., Zhang, J., Lian, S.: A novel color image encryption algorithm based on dna sequence operation and hyper-chaotic system. J. Syst. Softw. 85(2), 290–299 (2012)

    Article  Google Scholar 

  15. Zhang, Q., Guo, L., Wei, X.: Image encryption using dna addition combining with chaotic maps. Math. Comput. Model. 11–12(52), 2028–2035 (2010)

    Article  MathSciNet  Google Scholar 

  16. Hermassi, H., Belazi, A., Rhouma, R., Belghith, S.: Security analysis of an image encryption algorithm based on a DNA addition combining with chaotic maps. Multimed. Tools Appl. (2013). doi:10.1007/s11042-013-1533-6

  17. Patidar, V., Pareek, N.K., Sud, K.K.: A new substitution diffusion based image cipher using chaotic standard and logistic maps. Commun. Nonlinear Sci. Numer. Simul. 14, 3056–3075 (2009)

    Article  Google Scholar 

  18. Rhouma, R., Solak, E., Belghith, S.: Cryptanalysis of a new substitution–diffusion based image cipher. Commun. Nonlinear Sci. Numer. Simul. 15(7), 1887–1892 (2009)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Syscom Laboratory, National School of Engineers Tunis ENIT, Tunis, Tunisia

    Akram Belazi, Houcemeddine Hermassi, Rhouma Rhouma & Safya Belghith

Authors
  1. Akram Belazi
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  2. Houcemeddine Hermassi
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  3. Rhouma Rhouma
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  4. Safya Belghith
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Correspondence to Houcemeddine Hermassi.

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Belazi, A., Hermassi, H., Rhouma, R. et al. Algebraic analysis of a RGB image encryption algorithm based on DNA encoding and chaotic map. Nonlinear Dyn 76, 1989–2004 (2014). https://doi.org/10.1007/s11071-014-1263-y

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  • DOI: https://doi.org/10.1007/s11071-014-1263-y

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