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An efficient construction of substitution box with fractional chaotic system

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Abstract

In this article, we have presented an innovative formation of nonlinear element of block cipher. The suggested construction is chaos based, where we used fractional Rössler chaotic system. We have studied various features of our proposed nonlinear component. The outcomes of the investigations validate that the designed cryptosystem is consistent for secure communication.

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References

  1. Lorenz, E.N.: Deterministic non-periodic flow. J. Atmos. Sci. 20, 130–141 (1963)

    Article  Google Scholar 

  2. Rössler, O.E.: An equation for continuous chaos. Phys. Lett. A 57, 397–398 (1976)

    Article  Google Scholar 

  3. Rössler, O.E.: Continuous chaos four prototype equations. Ann N Y Acad Sci 316, 376–392 (1979)

    Article  Google Scholar 

  4. Chen, G., Ueta, T.: Yet another chaotic attractor. Int. J. Bifurcat. Chaos 9, 1465–1466 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. Li, H., Liao, X., Lei, X.: Two fuzzy control schemes for Lorenz-Stenflo chaotic system. J. Vib. Control 18, 1675–1682 (2012)

    Article  MathSciNet  Google Scholar 

  6. Kyrychko, Y.N., Hogan, S.J.: On the use of delay equations in engineering applications. J. Vib. Control 16, 943–960 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Van de Wouw, N., Verbeek, G., Van Campen, D.H.: Nonlinear parametric identification using chaotic data. J. Vib. Control 1, 291–305 (1995)

    Article  Google Scholar 

  8. Shannon, C.E.: A mathematical theory of communication. Bell. Syst. Tech. J. 27, 379–423 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  9. Shannon, C.E.: Communication theory of secrecy systems. Bell. Syst. Tech. J. 28, 656–715 (1949)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. Sam, I.S., Devaraj, P., Bhuvaneswaran, R.S.: An intertwining chaotic maps based image encryption scheme. Nonlinear Dyn. 69, 1995–2007 (2012)

    Google Scholar 

  12. Li, S., Mou, X., Ji, Z., Zhang, J., Cai, Y.: High-performance multimedia encryption system based on chaos. Phys. Lett. A 307, 22–28 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Jing mei, L., Baodian, W., Xiang, G.: Cryptanalysis of Rijndael S-box and improvement. Appl. Math. Comput. 170, 958–975 (2005)

    Google Scholar 

  14. Wang, Y., Wong, K.W., Liao, X., Xiang, T.: A block cipher with dynamic S-boxes based on tent map. Commun. Nonlinear Sci. Numer. Simul. 14, 3089–3099 (2009)

    Google Scholar 

  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, 571–579 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  17. Guoping, T., Xiaofeng, L., Yong, C.: A novel method for designing S-boxes based on chaotic maps. Chaos Solitons Fractals 23, 413–419 (2005)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  19. Jakimoski, G., Kocarev, L.: Chaos and cryptography: block encryption ciphers based on chaotic maps. IEEE Trans. Circuits Syst. 48, 163–169 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  20. Fatih, Ö., 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 

  21. Fatih, Ö., Sırma, Y.: Designing chaotic S-boxes based on time-delay chaotic system. Nonlinear Dyn. (2013). doi:10.1007/s11071-013-0987-4

  22. 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 

  23. Khan, M., Shah, T., Mahmood, H., Gondal, M.A.: An efficient technique for the construction of substitution box with chaotic partial differential equation. Nonlinear Dyn. 73, 1795–1801 (2013)

    Article  MathSciNet  Google Scholar 

  24. 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, 489–492 (2013)

    Article  MathSciNet  Google Scholar 

  25. Hussain, I., Shah, T., Gondal, M.A.: Image encryption algorithm based on PGL(2, GF(\(2^{8}\))) S-boxes and TD-ERCS chaotic sequence. Nonlinear Dyn. 70, 181–187 (2012)

    Article  MathSciNet  Google Scholar 

  26. Hussain, I., Shah, T.: S8 affine power affine S-boxes and their application. Neural Comput. Appl. 21, 377–383 (2012)

    Article  Google Scholar 

  27. Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: Construction of S8 Lui J S-boxes and their application. Comput. Math. Appl. 64, 2450–2458 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  28. Hussain, I., Shah, T., Gondal, M.A.: An efficient image encryption algorithm based on S8 S-box transformation and NCA map. Opt. Commun. 285, 4887–4890 (2012)

    Article  Google Scholar 

  29. Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: A projective general linear group based algorithm for the construction of substitution box for block ciphers. Neural Comput. Appl. 22, 1085–1093 (2013)

    Article  Google Scholar 

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Correspondence to Majid Khan.

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Khan, M., Shah, T. An efficient construction of substitution box with fractional chaotic system. SIViP 9, 1335–1338 (2015). https://doi.org/10.1007/s11760-013-0577-4

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  • DOI: https://doi.org/10.1007/s11760-013-0577-4

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