A Novel Design of Chaos Based S-Box Using Difference Distribution Table (CD S-Box)

  • Muhammad Asif Khan
  • Varun Jeoti
Part of the Communications in Computer and Information Science book series (CCIS, volume 420)


This research work reports the design methodology of a novel chaotic substitution box that is dynamically designed by systematically optimizing using DDT. DDT is a tool that helps in differential cryptanalysis of S-box. The proposed S-box shows very low differential probability as compared to other chaos based deigned S-box recently, while maintaining good cryptographic properties and linear approximation probability. Our proposed CD S-box achieves very low differential approximation probability of 8/256.


Substitution box chaos differential cryptanalysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Shannon, C.: Communication theory of secrecy systems. Bell System Technical Journal 28, 656–715 (1949)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Amigó, J.M., Kocarev, L., Szczepanski, J.: Theory and practice of chaotic cryptography. Physics Letters A 366, 211–216 (2007)CrossRefzbMATHGoogle Scholar
  3. 3.
    Kocarev, L.: Chaos-based cryptography: a brief overview, Circuits and Systems. IEEE Magazine 1, 6–21 (2001)Google Scholar
  4. 4.
    Kocarev, L., Jakimoski, G.: Logistic map as a block encryption algorithm. Physics Letters A 289, 199–206 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Masuda, N., Aihara, K.: Cryptosystems with discretized chaotic maps. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 49, 28–40 (2002)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Szczepanski, J., Amigo, J.M., Michalek, T., Kocarev, L.: Cryptographically secure substitutions based on the approximation of mixing maps. IEEE Transactions on Circuits and Systems I: Regular Papers 52, 443–453 (2005)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Behnia, S., Akhshani, A., Ahadpour, S., Mahmodi, H., Akhavan, A.: A. A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps. Physics Letters A 366, 391–396 (2007)CrossRefGoogle Scholar
  8. 8.
    Chen, G.: A novel heuristic method for obtaining S-boxes. Chaos, Solitons & Fractals 36, 1028–1036 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Chen, G., Chen, Y., Liao, X.: An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps. Chaos, Solitons & Fractals 31, 571–579 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Özkaynak, F., Özer, A.B.: A method for designing strong S-Boxes based on chaotic Lorenz system. Physics Letters A 374, 3733–3738 (2010)CrossRefzbMATHGoogle Scholar
  11. 11.
    Tang, G., Liao, X.: A method for designing dynamical S-boxes based on discretized chaotic map. Chaos, Solitons & Fractals 23, 1901–1909 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Tang, G., Liao, X., Chen, Y.: A novel method for designing S-boxes based on chaotic maps. Chaos, Solitons & Fractals 23, 413–419 (2005)CrossRefzbMATHGoogle Scholar
  13. 13.
    Clark, J.A., Jacob, J.L., Stepney, S.: The design of S-boxes by simulated annealing. New Gen. Comput. 23, 219–231 (2005)CrossRefzbMATHGoogle Scholar
  14. 14.
    Fuller, J., Millan, W., Dawson, E.: Multi-objective optimisation of bijective s-boxes. New Generation Computing 23, 201–218 (2005)CrossRefzbMATHGoogle Scholar
  15. 15.
    Laskari, E.C., Meletiou, G.C., Vrahatis, M.N.: Utilizing Evolutionary Computation Methods for the Design of S-Boxes. In: 2006 International Conference on Computational Intelligence and Security, pp. 1299–1302 (2006)Google Scholar
  16. 16.
    Millan, W.L.: How to Improve the Nonlinearity of Bijective S-boxes. In: Boyd, C., Dawson, E. (eds.) ACISP 1998. LNCS, vol. 1438, pp. 181–192. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  17. 17.
    Wang, Y., Wong, K.-W., Li, C., Li, Y.: A novel method to design S-box based on chaotic map and genetic algorithm. Physics Letters A 376, 827–833 (2012)CrossRefzbMATHGoogle Scholar
  18. 18.
    Biham, E., Shamir, A.: Differential Cryptanalysis of DES-like Cryptosystems. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 2–21. Springer, Heidelberg (1991)Google Scholar
  19. 19.
    Matsui, M.: Linear Cryptanalysis Method for DES Cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  20. 20.
    Schneier, B., Sutherland, P.: Applied cryptography: protocols, algorithms, and source code in C. John Wiley & Sons, Inc. (1995)Google Scholar
  21. 21.
    Bafghi, A.G., Safabakhsh, R., Sadeghiyan, B.: Finding the differential characteristics of block ciphers with neural networks. Information Sciences 178, 3118–3132 (2008)CrossRefGoogle Scholar
  22. 22.
    Asim, M., Jeoti, V.: Efficient and simple method for designing chaotic S-boxes. ETRI Journal 30, 170 (2008)CrossRefGoogle Scholar
  23. 23.
    Hussain, I., Shah, T., Mahmood, H., Gondal, M.: Construction of S8 Liu J S-boxes and their applications. Computers & Mathematics with Applications 64, 2450–2458 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    Bhattacharya, D., Bansal, N., Banerjee, A., RoyChowdhury, D.: A Near Optimal S-Box Design. In: McDaniel, P., Gupta, S.K. (eds.) ICISS 2007. LNCS, vol. 4812, pp. 77–90. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Muhammad Asif Khan
    • 1
  • Varun Jeoti
    • 1
  1. 1.Department of Electrical and Electronic EngineeringUniversiti Teknologi PETRONASTronohMalaysia

Personalised recommendations