Advertisement

Nonlinear Dynamics

, Volume 82, Issue 1–2, pp 107–117 | Cite as

A new image encryption scheme based on a simple first-order time-delay system with appropriate nonlinearity

  • Olfa Mannai
  • Rabei Bechikh
  • Houcemeddine Hermassi
  • Rhouma Rhouma
  • Safya Belghith
Original Paper

Abstract

Nonlinear delay differential system (NDDS) is a family of hyperchaotic systems, which has attracted much attention in the last years, especially in optics. The NDDS is often modeled by a time delay that occurs between the signals at the input and the output, and a nonlinearity introduced by a function \(F\). This paper introduces the Ikeda system that is considered system of infinite dimension and proposed an image encryption scheme by dynamic block. The encryption algorithm divides the image on dynamic blocks depending on the previous block cipher. The algorithm diffuses the plain image with bitwise XOR between each block and sequence generated by Ikeda system after quantification. Statistical analysis of the proposed encryption scheme demonstrates that this cryptosystem is secure enough to resist the brute-force attack, entropy attack, differential attack, chosen-plaintext attack, known-plaintext attack and statistical attack. In addition, the cryptosystem has high sensitivity of key and large space key.

Keywords

Cryptography Chaos Ikeda Image 

References

  1. 1.
    Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifur. Chaos 16(8), 2129–2151 (2006)MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Wang, X., Guo, K.: A new image alternate encryption algorithm based on chaotic map. Nonlinear Dyn. 76(4), 1943–1950 (2014)CrossRefGoogle Scholar
  3. 3.
    Abderrahim, N.W., Benmansour, F.Z., Seddiki, O.: A chaotic stream cipher based on symbolic dynamic description and synchronization. Nonlinear Dyn. doi: 10.1007/s11071-014-1432-z
  4. 4.
    Zhang, Y., Xiao, D.: An image encryption scheme based on rotation matrix bit-level permutation and block diffusion. Commun. Nonlinear Sci. Numer. Simul. 19(1), 74–82 (2014)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Chen, J., Zhu, Z., Fu, C., Yu, H.: A fast image encryption scheme with a novel pixel swapping-based confusion approach. Nonlinear Dyn. 77(4), 1191–1207 (2014)CrossRefGoogle Scholar
  6. 6.
    Zhu, Z., Zhang, W., Wong, K., Yu, H.: A chaos-based symmetric image encryption scheme using a bit-level permutation. Inf. Sci. 181, 1171–1186 (2011)CrossRefGoogle Scholar
  7. 7.
    Zhang, Y., Xiao, D.: Self-adaptive permutation and combined global diffusion for chaotic color image encryption. AEU Int. J. Electr. Commun. 68(4), 361–368 (2014)CrossRefGoogle Scholar
  8. 8.
    Norouzi, B., Mirzakuchaki, S., Seyedzadeh, S., Mosavi, M.: A simple, sensitive and secure image encryption algorithm based on hyper-chaotic system with only one round diffusion. Multimed. Tools Appl. doi: 10.1007/s11042-012-1292-9
  9. 9.
    Zhang, Y., Xiao, D., Shu, Y., Li, J.: A novel image encryption scheme based on a linear hyperbolic chaotic system of partial differential equations. Sig. Process. Image Commun. 28(3), 292–300 (2013)CrossRefGoogle Scholar
  10. 10.
    Hussain, I., Gondal, M.A.: An extended image encryption using chaotic coupled map and s-box transformation. Nonlinear Dyn. 76(2), 1355–1363 (2014)CrossRefGoogle Scholar
  11. 11.
    Song, C.-Y., Qiao, Y.-L., Zhang, X.-Z.: An image encryption scheme based on new spatiotemporal chaos. Optik Int. J. Light Electron Optics 124(18), 3329–3334 (2013)CrossRefGoogle Scholar
  12. 12.
    Zhang, Y.-Q., Wang, X.-Y.: Analysis and improvement of a chaos-based symmetric image encryption scheme using a bit-level permutation. Nonlinear Dyn. doi: 10.1007/s11071-014-1331-3
  13. 13.
    Zhang, Y., Xiao, D., Wen, W., Li, M.: Breaking an image encryption algorithm based on hyper-chaotic system with only one round diffusion process. Nonlinear Dyn. 76(3), 1645–1650 (2014)Google Scholar
  14. 14.
    Zhang, Y., Xiao, D.: Cryptanalysis of s-box-only chaotic image ciphers against chosen plaintext attack. Nonlinear Dyn. 72(4), 751–756 (2013)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Zhang, Y., Xiao, D., Wen, W., Nan, H.: Cryptanalysis of image scrambling based on chaotic sequences and Vigenere cipher. Nonlinear Dyn. 78(1), 235–240 (2014)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Su, M., Wen, W., Zhang, Y.: Security evaluation of bilateral-diffusion based image encryption algorithm. Nonlinear Dyn. 77(1–2), 243–246 (2014)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Zhang, Y., Xiao, D., Wen, W., Li, M.: Breaking an image encryption algorithm based on hyper-chaotic system with only one round diffusion process. Nonlinear Dyn. 76(3), 1645–1650 (2014)CrossRefGoogle Scholar
  18. 18.
    Mannai, O., Ben Jemaa, Z., Belghith, S.: Correlation properties of sequences generated by a simple first order scalar time-delay chaotic system. In: World Symposium on Computer Applications & Research (WSCAR), 18–20 January 2014, pp. 1–5. IEEE, Sousse (2014)Google Scholar
  19. 19.
    Farmer, J.: Chaotic attractors of an infinite-dimensional dynamical system. Phys. D 4, 366–393 (1982)MATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    Pesin, Y.: Characteristic Lyapunov exponents and smooth ergodic theory. Russ. Math. Surveys 32, 55–114 (1977)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Shanon, C.E.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28(4), 656–715 (1949)CrossRefGoogle Scholar
  22. 22.
    Chen, G., Mao, Y., Chui, C.K.: A symmetric image encryption based on 3D chaotic maps. Chaos Soliton Fractals 21, 749–761 (2004)MATHMathSciNetCrossRefGoogle Scholar
  23. 23.
    Hermassi, H., Rhouma, R., Belghith, S.: Security analysis of image cryptosystems only or partially based on a chaotic permutation. J. Syst. Softw. 85(9), 2133–2144 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Olfa Mannai
    • 1
  • Rabei Bechikh
    • 1
  • Houcemeddine Hermassi
    • 1
  • Rhouma Rhouma
    • 1
  • Safya Belghith
    • 1
  1. 1.École Nationale d’Ingénieurs de Tunis (ENIT)TunisTunisia

Personalised recommendations