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A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system

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Abstract

Substitution Box (S-Box) is one of the most significant structures used to create an encryption which is strong and resistant against attacks in block encryption algorithms. S-Box plays an important role in data encryption. This paper presents a novel S-Box generation algorithm design based on scaled Zhongtang chaotic system. In this study, a new random number generator which uses the new scaled Zhongtang chaotic system with very complicated and interesting dynamic features is designed; also, a new effective and strong S-Box design algorithm utilizing this RNG (random number generator) is developed. Bits generated by RNG are put to NIST tests and they passed all the NIST tests. Non-linearity, bit independence criteria, strict avalanche criteria, differential approximation probability performance tests are run on the proposed S-Box produced by new S-Box design algorithm. The proposed S-Box is compared with other studies available in the literature, and it is proved stronger and more effective.

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References

  1. Koyuncu, I., Ozcerit, A.T., Pehlivan, I.: Implementation of FPGA-based real time novel chaotic oscillator. Nonlinear Dyn. 77(2), 49–59 (2014)

    Article  MathSciNet  Google Scholar 

  2. Cicek, S., Uyaroglu, Y., Pehlivan, I.: Simulation and circuit implementation of sprott case H chaotic system and its synchronization application for secure communication systems. J. Circuits, Syst. Comput. 22(4), 1350022 (2013)

    Article  Google Scholar 

  3. Cavusoglu, U., Uyaroglu, Y., Pehlivan, I.: Desıgn of a continuous-time autonomous chaotic circuit and application of sıgnal masking. J. Fac. Eng. Archit. Gazi Univ. 29(1), 79–87 (2014)

    Google Scholar 

  4. Ott, E.: Chaos in Dynamical Systems, 2nd edn. Cambridge University Press, New York (2002)

    Book  MATH  Google Scholar 

  5. Shannon, C.E.: Science of chaos and cryptology. Bell Syst. Tech. J 28(6), 656 (1949)

    Article  Google Scholar 

  6. Amigo, J.M., Kocarev, L., Szczapanski, J.: Theory and practice of chaotic cryptography. Phys. Lett. A 366, 211–216 (2007)

    Article  MATH  Google Scholar 

  7. Jakimoski, G., Kocarev, L.: Chaos and cryptography: block encryption ciphers. IEEE Trans Circ Syst. 48(2), 163–169 (2001)

    Article  MATH  Google Scholar 

  8. Bakhache, B., Joseph, M.G., Safwan, E.A.: Improvement of the security of zigbee by a new chaotic algorithm. IEEE Syst. J. 8(4), 1024–1033 (2014)

    Article  Google Scholar 

  9. Wang, Y., Wong, K.W., Liao, X., Chen, G.: A new chaos-based fast image encryption algorithm. Appl. Soft Comput. 11(1), 514–522 (2011)

    Article  Google Scholar 

  10. Liu, Y., Tian, S., Hu, W., Xing, C.: Design and statistical analysis of a new chaotic block cipher for wireless sensor networks. Commun. Nonlinear Sci. Numer. Simul. 17(8), 3267–3278 (2012)

    Article  MathSciNet  Google Scholar 

  11. Angulo, J., Kussenar, E., Barthelemy, H., Duval, B.: A new oscillator-based RNG. IEEE Faible Tens. Faible Cons. doi:10.1109/FTFC.2012.6231723 (2012)

  12. Avaroglu, E., Turk, M.: RNG using multi-mode chaotic attractor. IEEE Signal Process. Commun. Appl. Conf. doi:10.1109/SIU.2013.6531520 (2013)

  13. Pareschı, F., Settı, G., Rovattı, R.: Implementation and testing of high-speed CMOS TRNGs based on chotic systems. IEEE Trans. Circuits Syst. 57(12), 3124–3137 (2010)

    Article  MathSciNet  Google Scholar 

  14. Ozkaynak, F.: Cryptographically secure random number generator with chaotic additional input. Nonlinear Dyn. 78(3), 2015–2020 (2014)

    Article  MathSciNet  Google Scholar 

  15. AES Algorithm. http://csrc.nist.gov/publications/fips/fips197/fips-197 (2001). Accessed 02 Jan.2016

  16. DES Algorithm. http://csrc.nist.gov/publications/fips/fips46-3/fips46-3 (1999). Accessed 02 Jan. 2016

  17. Brickell, E.F., Denning, D.E., Kent, S.T., Maher, D.P., Tuchman, W.: SKIPJACK review. The Skipjack Algorithm, Interim Report (1993)

  18. Jakimoski, G., Ljupco, K.: Chaos and cryptography: block encryption ciphers based on chaotic maps. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 48(2), 163–169 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  19. Liu, H., Abdurahman, K., Yujun, N.: Chaos-based color image block encryption scheme using S-box. AEU-Int. J. Electron. Commun. 68(7), 676–686 (2014)

    Article  Google Scholar 

  20. Tang, G., Liao, X., Chen, Y.: A novel method for designing S-boxes based on chaotic maps. Chaos, Solitons Fractals 23(2), 413–419 (2005)

    Article  MATH  Google Scholar 

  21. Tang, G., Xiaofeng, L.: 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 

  22. Peng, J., Jin, S., Lei, L., Liao, X.:Construction and analysis of dynamic S-boxes based on spatiotemporal chaos. In: Cognitive informatics cognitive computing, doi:10.1109/ICCI-CC.2012.6311160 (2012)

  23. Zaibi, G., Peyrard, F., Kachouri, A., Fournier Prunaret, D.: Efficient and secure chaotic S-Box for wireless sensor network. Secur. Commun. Netw. 7(2), 279–292 (2014)

    Article  Google Scholar 

  24. 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 

  25. Hussain, I., Tariq, S., Muhammad, A.G.: A novel approach for designing substitution-boxes based on nonlinear chaotic algorithm. Nonlinear Dyn. 70(3), 1791–1794 (2012)

    Article  MathSciNet  Google Scholar 

  26. Ozkaynak, F., Yavuz, S.: Designing chaotic S-boxes based on time-delay chaotic system. Nonlinear Dyn. 74(3), 551–557 (2013)

  27. Ozkaynak, F., Ozer, A.B.: A method for designing strong S-Boxes based on chaotic Lorenz system. Physics Lett. A 374(36), 3733–3738 (2010)

    Article  MATH  Google Scholar 

  28. Wang, Y., et al.: A block cipher with dynamic S-boxes based on tent map. Commun. Nonlinear Sci. Numer. Simul. 14(7), 3089–3099 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. Wang, Y., Xie, Q., Wu, Y., Du, B.: A software for S-box performance analysis and test. In: Electronic commerce and business intelligence, : ECBI 2009. International conference on IEEE, pp. 125–128 (2009)

  30. Chen, G.: A novel heuristic method for obtaining S-boxes. Chaos, Solitons Fractals 36(4), 1028–1036 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  31. Chen, G., Yong, C., Xiaofeng, L.: An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps. Chaos, Solitons Fractals 31(3), 571–579 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  32. Wu, Z., Wang, M., Jin, J., Feng, J.: A novel strange attractor and its dynamic analysis. J. Multimed. 9(3), 408–415 (2014)

    Article  Google Scholar 

  33. Pehlivan, I.: Four-scroll stellate new chaotic system. Optoelectron. Adv. Mater.-Rapid Commun. 5(9), 1003–1006 (2011)

    Google Scholar 

  34. Pehlivan, I., Wei, Z.: Analysis, nonlinear control and circuit design of an another strange chaotic system. Turk. J. Electr. Eng. Comput. Sci. 20(2), 1229–1239 (2012)

    Google Scholar 

  35. Pehlivan, I., Uyaroglu, Y.: A new 3D chaotic system with golden proportion equilibria: analysis and electronic circuit realization. Comput. Electr. Eng. 38(6), 1777–1784 (2012)

    Article  Google Scholar 

  36. Matlab. http://www.mathworks.com/. Accessed 05 Jan 2016

  37. A statistical test suite for random and pseudo RNGs for cryptographic applications. National institute of stand. and tech.,NIST-800-22, 2001. http://csrc.nist.gov/publications/nistpubs/800-22/sp-800-22-051501. Accessed 05 Jan 2016

  38. Webster, A. F., Stafford E. T.: On the design of S-boxes. In: Advances in cryptology-CRYPTO-85 proceedings. Springer, Berlin, Heidelberg (1986)

  39. Hussain, I., Shah, T., Mahmood, H., Gondal, M.A.: Construction of S 8 Liu J S-boxes and their applications. Comput. Math. Appl. 64(8), 2450–2458 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  41. Guesmi, R., Farah, M.A.B., Kachouri, A., Samet, M.: A novel design of Chaos based S-Boxes using genetic algorithm techniques. In: IEEE/ACS 11th international conference on computer systems and applications (AICCSA) pp. 678–684 (2014)

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Authors and Affiliations

  1. Department of Computer Engineering, Faculty Of Computer and Information Sciences Sakarya University, Serdivan, Sakarya, 54187, Turkey

    Ünal Çavuşoğlu & Ahmet Zengin

  2. Department of Electrical and Electronics Engineering, Faculty Of Technology Sakarya University, Serdivan, Sakarya, 54187, Turkey

    Ihsan Pehlivan & Sezgin Kaçar

Authors
  1. Ünal Çavuşoğlu
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  2. Ahmet Zengin
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  3. Ihsan Pehlivan
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  4. Sezgin Kaçar
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Correspondence to Ünal Çavuşoğlu.

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Çavuşoğlu, Ü., Zengin, A., Pehlivan, I. et al. A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system. Nonlinear Dyn 87, 1081–1094 (2017). https://doi.org/10.1007/s11071-016-3099-0

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  • DOI: https://doi.org/10.1007/s11071-016-3099-0

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