Advertisement

A novel method of dynamic S-box design based on combined chaotic map and fitness function

  • 24 Accesses

Abstract

This paper introduces a method of generating a strong S-box by using combined chaotic system and fitness function. Our method presents an algorithm which has two stages: static S-box generation and dynamic S-box optimization. Chaotic sequences generation, sequences discretization are involved in the first stage. Moreover, the proposed static S-box is converted into a dynamic S-box with the help of fitness function. The optimal S-box satisfies the following criteria: bijectivity, nonlinearity, strict avalanche criteria, output bits independence criterion, equiprobable inputs/outputs XOR distribution. Extensive experiments demonstrate that the proposed algorithm has excellent performance in cryptography and attacks resistance.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 199

This is the net price. Taxes to be calculated in checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

References

  1. 1.

    Belazi A, Khan M, Abd El-Latif AA, Belghith S (2016) Efficient cryptosystem approaches: S-boxes and permutationsubstitution-based encryption. Nonlinear Dyn. 87(1):1–25

  2. 2.

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

  3. 3.

    Chen X, Hu CJ (2017) Adaptive medical image encryption algorithm based on multiple chaotic mapping. Saudi J. Biol. Sci. 24(8):1821–1827

  4. 4.

    Daor J (1998) Joan Daemen, and Vincent Rijmen. AES proposal, Rijndael

  5. 5.

    Tarek Farah, Rhouma Rhouma, and Safya Belghith. A novel method for designing S-box based on chaotic map and TeachingLearning-Based Optimization. Nonlinear Dyn. 88(2):1059–1074, 2017.

  6. 6.

    Guo C (2008) A novel heuristic method for obtaining sboxes. Chaos Solitons and Fractals. 36(4):1028–1036

  7. 7.

    Hua Z, Zhou Y (2016) Image encryption using 2D logistic-adjusted-sine map. Inform. Sci. 339:237–253

  8. 8.

    Jakimoski G, Kocarev L (2001) Chaos and cryptography: block encryption ciphers based on chaotic maps. IEEE Trans. Circuits Syst. 48(2):163–169

  9. 9.

    Khan M (2015) A novel image encryption scheme based on multiple chaotic S-boxes. Nonlinear Dyn. 82(1–2):527–533

  10. 10.

    Khan M, Asghar Z (2018) A novel construction of substitution box for image encryption applications with Gingerbreadman chaotic map and S8permutation. Neural Comput. Applic. 29(4):993–999

  11. 11.

    Khan M, Shah T, Mahmood H, Gondal MA (2013) An efficient method for the construction of block cipher with multi-chaotic systems. Nonlinear Dyn. 71(3):489–492

  12. 12.

    P. A. W. Lewis, A. S. Goodman, and J. M. Miller (1969) A pseudo-random number generator for the system/360. IBM Syst. J. 8(2):136-146.

  13. 13.

    Matsui M (1994) Linear cryptanalysis method for DES Cipher. Advances in Cryptology — EUROCRYPT ’93. Springer Berlin Heidelberg. 386–397

  14. 14.

    Ozkaynak F, Ḉelik V, Özer AB (2017) A new S-box construction method based on the fractionalorder chaotic Chen system. Signal Image Video P. 11(4):659–664

  15. 15.

    Pak C, Huang L (2017) A new color image encryption using combination of the 1D chaotic map. Signal Process. 138:129–137

  16. 16.

    Tong XJ (2012) The novel bilateral diffusion image encryption algorithm with dynamical compound chaos. J Syst Software. 85(4):850–858

  17. 17.

    Tong X, Liu Y, Zhang M et al (2012) A novel image encryption scheme based on dynamical multiple Chaos and baker map[C]// international symposium on distributed Computing & Applications to business. IEEE Computer Society

  18. 18.

    Ullah A, Jamal SS, Shah T (2017) A novel construction of substitution box using a combination of chaotic maps with improved chaotic range. Nonlinear Dyn. 88(4):2757–2769

  19. 19.

    Ullah A, Jamal SS, Shah T (2018) A novel scheme for image encryption using substitution box and chaotic system. Nonlinear Dyn. 91(1):359–370

  20. 20.

    Wang Y, Wong KW, Li C, Li Y (2012) A novel method to design s-box based on chaotic map and genetic algorithm. Physics Letters A 376(67):827–833

  21. 21.

    Webster AF, Tavares SE (1986) On the design of S-Boxes. Springer, Berlin Heidelberg

  22. 22.

    Wu D, Weihong X (2011) Study on the relationship between S-box differential analysis and nonlinearity. Journal of Changsha University 25(5)

  23. 23.

    XiangYang X (2010) A new genetic algorithm and tabu search for S-box optimization. In International Conference on Computer Design and Applications. V4–492-V4–495

  24. 24.

    Zaibi G, Peyrard F, Kachouri A et al (2014) Efficient and secure chaotic S-box for wireless sensor network[J].  Secur Commun Netw. 7(2):279–292

  25. 25.

    Zhang T, Li S, Ge R, Yuan M, Ma Y (2016) A novel 1D hybrid chaotic map-basedimage compression and encryption using compressed sensing and fibonacci-lucas transform. Math. Probl. Eng.

  26. 26.

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

Download references

Acknowledgements

This work was supported by the following projects and foundations: project ZR2019MF054 supported by Shandong Provincial Natural Science Foundation, the Foundation of Science and Technology on Information Assurance Laboratory (No.KJ-17-004), 2017 Weihai University Co-construction Project, Equip Pre-research Projects of 2018, Foundation of China Academy of Space Technology (No. WT-TXYY/ WLZDFHJY003).

Author information

Correspondence to Xiaojun Tong.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhu, H., Tong, X., Wang, Z. et al. A novel method of dynamic S-box design based on combined chaotic map and fitness function. Multimed Tools Appl (2020) doi:10.1007/s11042-019-08478-0

Download citation

Keywords

  • Combined chaotic system
  • Substitution box
  • Fitness function
  • Dynamic S-box