Abstract
Substitution boxes are integral parts of most of the conventional block ciphering techniques such as DES, AES, IDEA, etc. The strengths of these encryption techniques solely depend upon the quality of their nonlinear S-boxes. Therefore, the construction of cryptographically strong S-boxes is always a challenge to build secure cryptosystems. In this paper, an efficient method for designing chaos-based cryptographic S-box is presented. The chaotically-modulated system trajectory of chaotic map is sampled and pretreated to generate an initial 8×8 S-box. Elements shuffling through random circular-rotation and zig-zag scan pattern are carried out to improve its quality. The experimental results of analyses such as bijectivity, nonlinearity, strict avalanche criterion, equiprobable input/output XOR distribution, etc., demonstrate that the proposed S-box has better cryptographic properties as compared to the recently proposed chaos-based S-boxes, which justify its effectiveness for the design of strong block cryptosystem.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Shannon, C.E.: Communication theory of secrecy systems. Bell Systems Technical Journal 28, 656–715 (1949)
Menezes, A.J., Oorschot, P.C.V., Vanstone, S.A.: Handbook of applied cryptography. CRC Press (1997)
Schneier, B.: Applied cryptography: protocols algorithms and source code in C. Wiley, New York (1996)
Biham, E., Shamir, A.: Differential cryptanalysis of DES-like cryptosystems. Journal of Cryptology 4(1), 3–72 (1991)
Dalai, D.K.: On some necessary conditions of boolean functions to resist algebraic attacks. PhD thesis, ISI Kolkata (2006)
Yin, Y., Li, X., Hu, Y.: Fast S-box security mechanism research based on the polymorphic cipher. Information Sciences 178(6), 1603–1610 (2008)
Bhattacharya, D., Bansal, N., Banaerji, A., Chowdhury, D.R.: A Near Optimal S-box Design. In: McDaniel, P., Gupta, S.K. (eds.) ICISS 2007. LNCS, vol. 4812, pp. 77–90. Springer, Heidelberg (2007)
Szaban, M., Seredynski, F.: Designing cryptographically strong S-boxes with the use of cellular automata. Annales UMCS Informatica Lublin-Polonia Sectio AI 8(2), 27–41 (2008)
Detombe, J., Tavares, S.: Constructing large cryptographically strong S-boxes. In: Zheng, Y., Seberry, J. (eds.) AUSCRYPT 1992. LNCS, vol. 718, pp. 165–181. Springer, Heidelberg (1993)
Chen, G.: A novel heuristic method for obtaining S-boxes. Chaos, Solitons & Fractals 36, 1028–1036 (2008)
Clark, J.A., Jacob, J.L., Stepney, S.: The Design of S-boxes by simulated annealing. New Generation Computing 23(3), 219–231 (2005)
Karaahmetoglu, O., Sakalli, M.T., Bulus, E., Tutanescu, I.: A new method to determine algebraic expression of power mapping based S-boxes. Information Processing Letters 113, 229–235 (2013)
Jakimoski, G., Kocarev, L.: Chaos and cryptography: Block encryption ciphers based on chaotic maps. IEEE Transaction on Circuits Systems 48(2), 163–169 (2001)
Tang, G., Liao, X., Chen, Y.: A novel method for designing S-boxes based on chaotic maps. Chaos, Solitons Fractals 23, 413–419 (2005)
Chen, G., Chen, Y., Liao, X.: An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps. Chaos Solitons Fractals 31, 571–577 (2007)
Asim, M., Jeoti, V.: Efficient and simple method for designing chaotic S-boxes. ETRI Journal 30(1), 170–172 (2008)
Yin, R., Yuan, J., Wang, J., Shan, X., Wang, X.: Designing key-dependent chaotic S-box with large key space. Chaos Solitons Fractals 42, 2582–2589 (2009)
Wang, Y., Wong, K.W., Liao, X., Xiang, T.: A block cipher with dynamic S-boxes based on tent map. Communications in Nonlinear Science and Numerical Simulations 14, 3089–3099 (2009)
Özkaynak, F., Özer, A.B.: A method for designing strong S-boxes based on chaotic Lorenz system. Physics Letters A 374, 3733–3738 (2010)
May, R.M.: Simple mathematical model with very complicated dynamics. Nature 261, 459–467 (1967)
Li, S., Chen, G., Mou, X.: On the dynamical degradation of digital piecewise linear chaotic maps. International Journal of Bifurcation and Chaos 15(10), 3119–3151 (2005)
Wallace, G.K.: The JPEG still picture compression standard. IEEE Transaction on Consumer Electronics 38, 18–34 (1992)
Webster, A.F., Tavares, S.: On the design of S-boxes. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 523–534. Springer, Heidelberg (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ahmad, M., Chugh, H., Goel, A., Singla, P. (2013). A Chaos Based Method for Efficient Cryptographic S-box Design. In: Thampi, S.M., Atrey, P.K., Fan, CI., Perez, G.M. (eds) Security in Computing and Communications. SSCC 2013. Communications in Computer and Information Science, vol 377. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40576-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-40576-1_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40575-4
Online ISBN: 978-3-642-40576-1
eBook Packages: Computer ScienceComputer Science (R0)