Nonlinear Dynamics

, Volume 88, Issue 4, pp 2757–2769 | Cite as

A novel construction of substitution box using a combination of chaotic maps with improved chaotic range

Original Paper

Abstract

The influential application of substitution boxes in secure communication and multimedia security attracted researchers to construct more robust substitution boxes. The advantage of using chaos in the secure communication is to get additional unpredictability and randomness in data. In this paper, substitution boxes are constructed with the help of chaotic system and linear fractional transformation. The 256 distinct values of each substitution box are then checked with the help of different available algebraic and statistical analyses. These tests evaluate the strength and application of substitution boxes in different encryption techniques. The results indicate the strength of anticipated technique.

Keywords

Logistic–tent map Chaotic range Group action S-box 

References

  1. 1.
    Chen, G., Ueta, T.: Yet another chaotic attractor. Int. J. Bifurc. Chaos 9(07), 1465–1466 (1999)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Shannon, C.E.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28(4), 656–715 (1949)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Hussain, I., Gondal, M.A.: An extended image encryption using chaotic coupled map and S-box transformation. Nonlinear Dyn. 76, 1355–1363 (2014)CrossRefGoogle Scholar
  4. 4.
    Wong, K.W.: On the security of a spatiotemporal chaotic cryptosystem. Phys. Lett. A 298, 238 (2002)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Sam, I.S., Devaraj, P., Bhuvaneswaran, R.S.: An intertwining chaotic map based image encryption scheme. Nonlinear Dyn. 69(4), 1995–2007 (2012)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hussain, I., Tariq Shah, T.: Literature survey on nonlinear components and chaotic nonlinear components of block ciphers. Nonlinear Dyn. 74, 869–904 (2013)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Khan, M., Shah, T., Batool, S.I.: Construction of S-box based on chaotic Boolean functions and its application in image encryption. Neural Comput. Appl. 27(3), 677–685 (2016)CrossRefGoogle Scholar
  8. 8.
    Jakimoski, G., Kocarev, L.: Chaos and cryptography: block encryption ciphers based on chaotic maps. IEEE Trans. Circuits Syst. 48(2), 163 (2001)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Belazi, A., Khan, M., El-Latif, A.A.A., Belghith, S.: Efficient cryptosystem approaches: S-boxes and permutation-substitution-based encryption. Nonlinear Dyn. 87, 337–361 (2017)CrossRefGoogle Scholar
  10. 10.
    Khan, M., Shah, T., Gondal, M.A.: An efficient technique for the construction of substitution box with chaotic partial differential equation. Nonlinear Dyn. 73, 1795–1801 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    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)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Adams, C., Tavares, S.: Chapter-4: Advances in cryptology. In: Proceedings of CRYPTO_89. Lecture Notes in Computer Science, pp. 612–615 (1989)Google Scholar
  13. 13.
    Webster, A.F., Tavares, S.: Chapter-3: Advances in cryptology. In: Proceedings of CRYPTO_85. Lecture Notes in Computer Science, pp. 523-534 (1986)Google Scholar
  14. 14.
    Guoping, T., Xiaofeng, L., Yong, C.: A novel method for designing S-boxes based on chaotic maps. Chaos Solitons Fractals 23, 413 (2005)CrossRefMATHGoogle Scholar
  15. 15.
    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 (2007)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Alkhaldi, A.H., Hussain, I., Gondal, M.A.: A novel design for the construction of safe S-boxes based on TDERC sequence. Alex. Eng. J. 54, 65–69 (2015)CrossRefGoogle Scholar
  17. 17.
    Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: Efficient method for designing chaotic S-boxes based on generalized Baker’s map and TDERC chaotic sequence. Nonlinear Dyn. 74, 271–275 (2013)MathSciNetCrossRefGoogle Scholar
  18. 18.
    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(3), 2303–2311 (2012)MathSciNetCrossRefGoogle Scholar
  19. 19.
    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. 22, 1085–1093 (2013)CrossRefGoogle Scholar
  20. 20.
    Farwa, S., Shah, T., Idrees, L.: A highly nonlinear S-box based on a fractional linear transformation. SpringerPlus 5(1), 1658 (2016)CrossRefGoogle Scholar
  21. 21.
    Wang, X.Y.: Chaos in the Complex Nonlinearity System. Electronics Industry Press, Beijing (2003)Google Scholar
  22. 22.
    Zhou, Y., Bao, L., Chen, C.L.P.: A new 1D chaotic system for image encryption. Sig. Process. 97, 172–182 (2014)Google Scholar
  23. 23.
    Biham, E., Shamir, A.: Differential cryptanalysis of DES like cryptosystems. J. Cryptol. 4(1), 3–72 (1991)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Detombe, J., Tavares, S.: Chapter-7: Advances in cryptology. In: Proceedings of CRYPTO_92. Lecture Notes in Computer Science (1992)Google Scholar
  25. 25.
    Dawson, M., Tavares, S.: Chapter-4: Advances in cryptology. In: Proceedings of EURO-CRYPT_91. Lecture Notes in Computer Science, pp. 352–367 (1991)Google Scholar
  26. 26.
    Feng, D., Wu, W.: Design and Analysis of Block Ciphers. Tsinghua University Press, Beijing (2000)Google Scholar
  27. 27.
    Matsui, M.: Linear cryptanalysis method of DES cipher. In: Advances in cryptology, Proceeding of the Eurocrypt’93. Lecture Notes Computer Science, vol. 765, pp. 386–397 (1994)Google Scholar
  28. 28.
    Cui, Lingguo, Cao, Yuanda: A new S-box structure named affine-power-affine. Int. J. Innov. Comput. Inf. Control 3, 751–759 (2007)Google Scholar
  29. 29.
    Skipjack and Kea: Algorithm Specifications Version 2, 1–23. http://csrc.nist.gov/CryptoToolkit/ (1998)
  30. 30.
    Daemen, J., Rijmen, V.: AES Proposal: Rijndael, AES Algorithm Submission (1999)Google Scholar
  31. 31.
    Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: Generalized majority logic criterion to analyze the statistical strength of S-boxes. Z. Naturforsch. A 67a, 282–288 (2012)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan

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