Skip to main content
Log in

Designing chaotic S-boxes based on time-delay chaotic system

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

Abstract

S-box structures used in the encryption architecture are of great importance for constructing powerful block encryption systems, which hold an important place in modern cryptology. The design of S-boxes with sound cryptographic characteristics is of utmost importance for constructing powerful encryption systems. In this study, an S-box design algorithm based on time-delay chaotic systems is proposed. The proposed algorithm is considered relative to other algorithms in the literature as more useful according to such criteria as simplicity and efficient implementation. Theoretical analysis and computer simulations demonstrated that the proposed algorithm meets all the performance requirements for the S-box design criteria, and also verified the efficient and practical structure of the algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

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

Similar content being viewed by others

References

  1. Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurc. Chaos Appl. Sci. Eng. 16(8), 2129–2153 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Amigo, J.M., Kocarev, L., Szczapanski, J.: Theory and practice of chaotic cryptography. Phys. Lett. A 336, 211–216 (2007)

    Article  Google Scholar 

  3. Jakimoski, G., Kocarev, L.: Chaos and cryptography: block encryption ciphers. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(2), 163–169 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Tang, G., Liao, X., Chen, Y.: A novel method for designing S-boxes based on chaotic maps. Chaos Solitons Fractals 23, 413–419 (2005)

    Article  MATH  Google Scholar 

  5. Tang, G., Liao, X.: A method for designing dynamical S-boxes based on discretized chaotic map. Chaos Solitons Fractals 23(5), 1901–1909 (2005)

    MathSciNet  MATH  Google Scholar 

  6. Chen, G., Chen, Y., Liao, X.: An extended method for obtaining S-boxes based on 3-dimensional chaotic baker maps. Chaos Solitons Fractals 31, 571–579 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen, G.: A novel heuristic method for obtaining S-boxes. Chaos Solitons Fractals 36, 1028–1036 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Özkaynak, F., Özer, A.B.: A method for designing strong S-boxes based on chaotic Lorenz system. Phys. Lett. A 374, 3733–3738 (2010)

    Article  MATH  Google Scholar 

  9. Khan, M., Shah, T., Mahmood, H., Gondal, M.A.: An efficient method for the construction of block cipher with multi-chaotic systems. Nonlinear Dyn. 71(3), 489–492 (2013)

    Article  MathSciNet  Google Scholar 

  10. Khan, M., Shah, T., Mahmood, H., Gondal, M.A., Hussain, I.: A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems. Nonlinear Dyn. 70, 2303–2311 (2012)

    Article  MathSciNet  Google Scholar 

  11. Hussain, I., Shah, T., Gondal, M.A.: A novel approach for designing substitution-boxes based on nonlinear chaotic algorithm. Nonlinear Dyn. 70, 1791–1794 (2012)

    Article  MathSciNet  Google Scholar 

  12. Sprott, J.C.: A simple chaotic delay differential equation. Phys. Lett. A 366, 397–402 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Uçar, A.: A prototype model for chaos studies. Int. J. Eng. Sci. 40, 251–258 (2002)

    Article  MATH  Google Scholar 

  14. Prokhorow, M.D., Ponomarenko, V.I.: Encryption and decryption of information in chaotic communication systems governed by delay-differential equations. Chaos Solitons Fractals 35, 871–877 (2008)

    Article  Google Scholar 

  15. Tang, Y., Wang, Z., Fang, J.: Image encryption using chaotic coupled map lattices with time-varying delays. Commun. Nonlinear Sci. Numer. Simul. 15, 2456–2468 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Sprott, J.C.: Elegant Chaos Algebraically Simple Chaotic Flow. World Scientific, Singapore (2010)

    Book  Google Scholar 

  17. Wang, Y., Xie, Q., Wu, Y., Du, B.: A software for S-box performance analysis and test. In: 2009 International Conference on Electronic Commerce and Business Intelligence, Beijing, China, pp. 125–128 (2009)

    Chapter  Google Scholar 

  18. Webster, A., Tavares, S.: On the design of S-boxes. In: Advances in Cryptology: Proc. of Crypto’85, Santa Barbara, USA. Lecture Notes in Computer Science, vol. 218, pp. 523–534 (1986)

    Chapter  Google Scholar 

  19. Adams, C., Tavares, S.: Good S-boxes are easy to find. In: Advances in Cryptology: Proc. of Crypto’89, Santa Barbara, USA. Lecture Notes in Computer Science, vol. 435, pp. 612–615 (1989)

    Chapter  Google Scholar 

  20. Biham, E., Shamir, A.: Differential cryptanalysis of DES-like cryptosystems. J. Cryptol. 4(1), 3–72 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  21. Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, London (1993)

    MATH  Google Scholar 

  22. Sprott, J.C.: Chaos and Time-Series Analysis. Oxford University Press, London (2003)

    MATH  Google Scholar 

  23. Ikeda, K.: Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Opt. Commun. 30, 257{261 (1979)

    Article  Google Scholar 

  24. Verhulst, P.F.: Notice sur la loi que la population poursuit dans son accroissement. Corresp. Math. Phys. 10, 113–121 (1838)

    Google Scholar 

  25. Cusick, T.W., Stanica, P.: Cryptographic Boolean Functions and Applications. Elsevier, Amsterdam (2009)

    Google Scholar 

  26. Youssef, A.M., Tavares, S.E., Gong, G.: On some probabilistic approximations for AES-like S-boxes. Discrete Math. 306(16), 2016–2020 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  27. Youssef, A.M., Tavares, S.E.: Affine equivalence in the AES round function. Discrete Appl. Math. 148(2), 161–170 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  28. Jing-mei, L., Bao-dian, W., Xiang-guo, C., Xin-mei, W.: Cryptanalysis of Rijndael S-box and improvement. Appl. Math. Comput. 170(2), 958–975 (2005)

    Article  MathSciNet  Google Scholar 

  29. Bard, G.V.: Algebraic Cryptanalysis. Springer, Berlin (2009)

    Book  MATH  Google Scholar 

  30. Hussain, I., Shah, T., Mahmood, H., Gondal, M.A.: A projective general linear group based algorithm for the construction of substitution box for block ciphers. Neural Comput. Appl. doi:10.1007/s00521-012-0870-0

  31. Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: Analysis of S-box in image encryption using root mean square error method. Z. Naturforsch. 67, 327–332 (2012)

    Article  Google Scholar 

  32. Özkaynak, F., Özer, A.B.: A novel algorithm for strengthening of chaos based S-box generators. In: 2010 National Conference on Electrical, Electronics and Computer Engineering (ELECO 2010), Bursa, pp. 553–557 (2010). Art. No. 5698211

    Google Scholar 

  33. Hussain, I., Shah, T., Gondal, M.A.: An efficient image encryption algorithm based on S8 S-box transformation and NCA map. Optics Communications 285(24), 4887–4890

  34. Hussain, I.: A novel approach of audio watermarking based on S-box transformation. Math. Comput. Model. 57(3–4), 963–969 (2013)

    Article  Google Scholar 

  35. Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: An efficient approach for the construction of LFT S-boxes using chaotic logistic map. Nonlinear Dyn. 71, 133–140 (2013)

    Article  MathSciNet  Google Scholar 

  36. Hussain, I., Shah, T., Gondal, M.A.: A novel approach for designing substitution-boxes based on nonlinear chaotic algorithm. Nonlinear Dyn. 70, 1791–1794 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fatih Özkaynak.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Özkaynak, F., Yavuz, S. Designing chaotic S-boxes based on time-delay chaotic system. Nonlinear Dyn 74, 551–557 (2013). https://doi.org/10.1007/s11071-013-0987-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-013-0987-4

Keywords

Navigation