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

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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.

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References

  1. Chen, G., Ueta, T.: Yet another chaotic attractor. Int. J. Bifurc. Chaos 9(07), 1465–1466 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Shannon, C.E.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28(4), 656–715 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hussain, I., Gondal, M.A.: An extended image encryption using chaotic coupled map and S-box transformation. Nonlinear Dyn. 76, 1355–1363 (2014)

    Article  Google Scholar 

  4. Wong, K.W.: On the security of a spatiotemporal chaotic cryptosystem. Phys. Lett. A 298, 238 (2002)

    Article  MathSciNet  Google Scholar 

  5. Sam, I.S., Devaraj, P., Bhuvaneswaran, R.S.: An intertwining chaotic map based image encryption scheme. Nonlinear Dyn. 69(4), 1995–2007 (2012)

    Article  MathSciNet  Google Scholar 

  6. Hussain, I., Tariq Shah, T.: Literature survey on nonlinear components and chaotic nonlinear components of block ciphers. Nonlinear Dyn. 74, 869–904 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  8. Jakimoski, G., Kocarev, L.: Chaos and cryptography: block encryption ciphers based on chaotic maps. IEEE Trans. Circuits Syst. 48(2), 163 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  12. Adams, C., Tavares, S.: Chapter-4: Advances in cryptology. In: Proceedings of CRYPTO_89. Lecture Notes in Computer Science, pp. 612–615 (1989)

  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)

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

    Article  MATH  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 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  20. Farwa, S., Shah, T., Idrees, L.: A highly nonlinear S-box based on a fractional linear transformation. SpringerPlus 5(1), 1658 (2016)

    Article  Google Scholar 

  21. Wang, X.Y.: Chaos in the Complex Nonlinearity System. Electronics Industry Press, Beijing (2003)

    Google Scholar 

  22. Zhou, Y., Bao, L., Chen, C.L.P.: A new 1D chaotic system for image encryption. Sig. Process. 97, 172–182 (2014)

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

    Article  MathSciNet  MATH  Google Scholar 

  24. Detombe, J., Tavares, S.: Chapter-7: Advances in cryptology. In: Proceedings of CRYPTO_92. Lecture Notes in Computer Science (1992)

  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)

  26. Feng, D., Wu, W.: Design and Analysis of Block Ciphers. Tsinghua University Press, Beijing (2000)

    Google Scholar 

  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)

  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. Skipjack and Kea: Algorithm Specifications Version 2, 1–23. http://csrc.nist.gov/CryptoToolkit/ (1998)

  30. Daemen, J., Rijmen, V.: AES Proposal: Rijndael, AES Algorithm Submission (1999)

  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 

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

    Atta Ullah, Sajjad Shaukat Jamal & Tariq Shah

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  1. Atta Ullah
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  2. Sajjad Shaukat Jamal
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  3. Tariq Shah
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Correspondence to Atta Ullah.

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Ullah, A., Jamal, S.S. & Shah, T. A novel construction of substitution box using a combination of chaotic maps with improved chaotic range. Nonlinear Dyn 88, 2757–2769 (2017). https://doi.org/10.1007/s11071-017-3409-1

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  • DOI: https://doi.org/10.1007/s11071-017-3409-1

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