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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
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)
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)
Burnett, L.D.: Heuristic Optimization of Boolean Functions and Substitution Boxes for Cryptography. Ph.D. thesis, Queensland University of Technology (2005)
Carlet, C., Ding, C.: Nonlinearities of s-boxes. Finite Fields Appl. 13(1), 121–135 (2007)
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)
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)
Daemen, J., Rijmen, V.: Aes proposal: Rijndael (1999)
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)
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)
Durillo, J.J., Nebro, A.J.: jmetal: A java framework for multi-objective optimization. Adv. Eng. Softw. 42(10), 760–771 (2011)
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)
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)
Ivanov, G., Nikolov, N., Nikova, S.: Reversed genetic algorithms for generation of bijective s-boxes with good cryptographic properties. Crypt. Commun., 1–30 (2016)
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)
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)
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)
Parker, M.: Generalised s-box nonlinearity. NESSIE Public Document NES/DOC/UIB/WP5/020/A (2003)
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)
Shannon, C.E.: Communication theory of secrecy systems*. Bell Syst. Tech. J. 28(4), 656–715 (1949)
Srinivas, N., Deb, K.: Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol. Comput. 2(3), 221–248 (1994)
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)
Yu, W., Cao, J.: Cryptography based on delayed chaotic neural networks. Phys. Lett. A 356(4–5), 333–338 (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Kapuściński, T., Nowicki, R.K., Napoli, C. (2016). Application of Genetic Algorithms in the Construction of Invertible Substitution Boxes. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2016. Lecture Notes in Computer Science(), vol 9692. Springer, Cham. https://doi.org/10.1007/978-3-319-39378-0_33
Download citation
DOI: https://doi.org/10.1007/978-3-319-39378-0_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-39377-3
Online ISBN: 978-3-319-39378-0
eBook Packages: Computer ScienceComputer Science (R0)