Application of Genetic Algorithms in the Construction of Invertible Substitution Boxes

  • Tomasz Kapuściński
  • Robert K. Nowicki
  • Christian Napoli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9692)

Abstract

Existing literature shows that genetic algorithms can be successfully used for automated construction of S-boxes. In this paper we show the usage of genetic algorithm, more specifically NSGA-II, as an aid in designing and testing of invertible substitution boxes which are special case of substitution boxes. Many cryptographic properties of S-boxes are often contradicting each other. It is therefore difficult to find an optimal solution. NSGA-II proved to be a valuable tool in finding a range of solutions from which we can later select an appropriate S-box for a cipher. We also show that we can use NSGA-II to test integration of S-boxes with a cipher and automatically reject S-boxes which make the cipher weak.

Keywords

NSGA-II Substitution box Invertible S-box Cryptography Genetic algorithm 

References

  1. 1.
    Aghdam, M.H., Heidari, S.: Feature selection using particle swarm optimization in text categorization. J. Artif. Intell. Soft Comput. Res. 5(4), 231–238 (2015)CrossRefGoogle Scholar
  2. 2.
    Aguirre, H., Okazaki, H., Fuwa, Y.: An evolutionary multiobjective approach to design highly non-linear boolean functions. In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, GECCO 2007, pp. 749–756. ACM, New York (2007)Google Scholar
  3. 3.
    Burnett, L.D.: Heuristic Optimization of Boolean Functions and Substitution Boxes for Cryptography. Ph.D. thesis, Queensland University of Technology (2005)Google Scholar
  4. 4.
    Carlet, C., Ding, C.: Nonlinearities of s-boxes. Finite Fields Appl. 13(1), 121–135 (2007)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Chafekar, D., Xuan, J., Rasheed, K.: Constrained multi-objective optimization using steady state genetic algorithms. In: Cantú-Paz, E., et al. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 813–824. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Chen, Q., Abercrombie, R.K., Sheldon, F.T.: Risk assessment for industrial control systems quantifying availability using mean failure cost (mfc). J. Artif. Intell. Soft Comput. Res. 5(3), 205–220 (2015)CrossRefGoogle Scholar
  7. 7.
    Daemen, J., Rijmen, V.: Aes proposal: Rijndael (1999)Google Scholar
  8. 8.
    Dawson, M.H., Tavares, S.: An expanded set of s-box design criteria based on information theory and its relation to differential-like attacks. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 352–367. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  9. 9.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  10. 10.
    Durillo, J.J., Nebro, A.J.: jmetal: A java framework for multi-objective optimization. Adv. Eng. Softw. 42(10), 760–771 (2011)CrossRefGoogle Scholar
  11. 11.
    Durillo, J.J., Nebro, A.J., Luna, F., Alba, E.: On the effect of the steady-state selection scheme in multi-objective genetic algorithms. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, J.-K., Sevaux, M. (eds.) EMO 2009. LNCS, vol. 5467, pp. 183–197. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Hayashi, Y., Tanaka, Y., Takagi, T., Saito, T., Iiduka, H., Kikuchi, H., Bologna, G., Mitra, S.: Recursive-rule extraction algorithm with J48graft and applications to generating credit scores. J. Artif. Intell. Soft Comput. Res. 6(1), 35–44 (2016)CrossRefGoogle Scholar
  13. 13.
    Ivanov, G., Nikolov, N., Nikova, S.: Reversed genetic algorithms for generation of bijective s-boxes with good cryptographic properties. Crypt. Commun., 1–30 (2016)Google Scholar
  14. 14.
    Korytkowski, M., Gabryel, M., Rutkowski, L., Drozda, S.: Evolutionary methods to create interpretable modular system. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 405–413. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Li, C., Li, S., Zhang, D., Chen, G.: Cryptanalysis of a chaotic neural network based multimedia encryption scheme. In: Aizawa, K., Nakamura, Y., Satoh, S. (eds.) PCM 2004. LNCS, vol. 3333, pp. 418–425. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Lian, S.: A block cipher based on chaotic neural networks. Neurocomputing 72(4–6), 1296–1301 (2009). Brain Inspired Cognitive Systems (BICS 2006)/Interplay Between Natural and Artificial Computation (IWINAC 2007)CrossRefGoogle Scholar
  17. 17.
    Parker, M.: Generalised s-box nonlinearity. NESSIE Public Document NES/DOC/UIB/WP5/020/A (2003)Google Scholar
  18. 18.
    Serdah, A.M., Ashour, W.M.: Clustering large-scale data based on modified affinity propagation algorithm. J. Artif. Intell. Soft Comput. Res. 6(1), 23–33 (2016)CrossRefGoogle Scholar
  19. 19.
    Shannon, C.E.: Communication theory of secrecy systems*. Bell Syst. Tech. J. 28(4), 656–715 (1949)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Srinivas, N., Deb, K.: Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol. Comput. 2(3), 221–248 (1994)CrossRefGoogle Scholar
  21. 21.
    Szarek, A., Korytkowski, M., Rutkowski, L., Scherer, R., Szyprowski, J.: Application of neural networks in assessing changes around implant after total hip arthroplasty. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part II. LNCS, vol. 7268, pp. 335–340. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  22. 22.
    Yu, W., Cao, J.: Cryptography based on delayed chaotic neural networks. Phys. Lett. A 356(4–5), 333–338 (2006)CrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Tomasz Kapuściński
    • 1
  • Robert K. Nowicki
    • 1
  • Christian Napoli
    • 2
  1. 1.Institute of Computational IntelligenceCzestochowa University of TechnologyCzestochowaPoland
  2. 2.Department of Mathematics and InformaticsUniversity of CataniaCataniaItaly

Personalised recommendations