Abstract
A substitution box is used to induce nonlinearity in plaintext for encryption systems. Recently, the application of chaotic maps to encryption applications has resulted in some interesting nonlinear transformations. In this paper, we propose an efficient method to design nonlinear components for block ciphers that are based on TD-ERCS chaotic sequence. The new substitution box is analyzed for nonlinearity, bit independence, strict avalanche criterion, generalized majority logic criterion, and differential and linear approximation probabilities. The results show high resistance to differential and linear cryptanalysis in comparison to some recently proposed chaotic substitution boxes.
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Burr, W.E.: Selecting the advanced encryption standard. IEEE Secur. Priv. 1(2), 43–52 (2003)
Smid, M.E., Branstad, D.K.: Data encryption standard: past and future. Proc. IEEE 76(5), 550–559 (1988)
Hong, Z., Ji-xue, D.: Chaos theory and its application in modern cryptography. In: Computer Application and System Modeling (ICCASM), 2010 International Conference, vol. 7, pp. V7-332–V7-334 (2010)
Ghnaim, W.A.-E., Ghali, N.I., Hassanien, A.E.: Known-cipher text cryptanalysis approach for the data encryption standard technique. In: 2010 International Conference on Computer Information Systems and Industrial Management Applications (CISIM), pp. 600–603 (2010)
Hermelin, M., Nyberg, K.: Multidimensional linear distinguishing attacks and Boolean functions. Cryptogr. Commun. 4(1), 47–64 (2012)
Knellwolf, S., Meier, W.: High order differential attacks on stream ciphers. Cryptogr. Commun. 4(3–4), 203–215 (2012)
Nyberg, K.: Differentially uniform mappings for cryptography. In: Advances in Cryptology, Proc. Eurocrypt’93, LNCS, vol. 765, pp. 55–64 (1994)
Jakimoski, G., Kocarev, L.: Chaos and cryptography: block encryption ciphers based on chaotic maps. IEEE Trans. Circuits Syst. I 48(2), 163–169 (2001)
Li, S., Chen, G., Mou, X.: On the dynamical degradation of digital piecewise linear chaotic maps. Int. J. Bifurc. Chaos 15(10), 3119–3151 (2005)
Peitegen, H.-O., Jürgens, H., Saupe, D.: Chaos and Fractals—New Frontiers of Science, 2nd edn. Springer, Berlin (2004)
Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurc. Chaos 16(8), 2129–2151 (2006)
Chen, G., Chen, Y., Liao, X.: An extended method for obtaining S-boxes based on three-dimensional chaotic baker maps. Chaos Solitons Fractals 31, 571–579 (2007)
Tang, G., Liao, X., Chen, Y.: A novel method for designing S-boxes based on chaotic maps. Chaos Solitons Fractals 23, 413–419 (2005)
Ke-Hui, S., Guo-Qiang, T., Li-Yuan, S.: The complexity analysis of TD-ERCS discrete chaotic pseudo-random sequences. Acta Phys. Sin. 57(6), 3359–3366 (2008)
Kohda, T., Tsuneda, A.: Statistics of chaotic binary sequences. IEEE Trans. Inf. Theory 43, 104–120 (1997)
Sheng, L., Sun, K., Li, C.: Study of a discrete chaotic system based on tangent-delay for elliptic reflecting cavity and its properties. Acta Phys. Sin. 53, 2871–2876 (2004)
Sheng, L., Cao, L., Sun, K.: Pseudo-random number generator based on TD-ERCS chaos and its statistic characteristics analysis. Acta Phys. Sin. 54, 4031–4037 (2005)
Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: A projective general linear group based algorithm for the construction of substitution box for block ciphers. Neural Comput. Appl. (2012). doi:10.1007/s00521-012-0870-0
Hussain, I., Shah, T., Mahmood, H., Gondal, M.A.: A group theoretic approach to construct cryptographically strong substitution boxes. Neural Comput. Appl. (2012). doi:10.1007/s00521-012-0914-5
Shah, T., Hussain, I., Gondal, M.A.: Image encryption algorithm based on PGL(2,GF(28)) S-boxes and TD-ERCS chaotic sequence. Nonlinear Dyn. 70(1), 181–187 (2012)
Hussain, I., Shah, T., Mahmood, H., Gondal, M.A.: S8 affine power affine S-boxes and their application. Neural Comput. Appl. 21, 377–383 (2012)
Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: Construction of S8 Lui J S-boxes and their application. Comput. Math. Appl. 64(8), 2450–2458 (2012)
Hussain, I., Shah, T., Gondal, M.A.: An efficient image encryption algorithm based on S8 S-box transformation and NCA map. Opt. Commun. 285(24), 4887–4890 (2012)
Hussain, I., Shah, T., Gondal, M.A., Wang, Y.: Analyses of SKIPJACK S-box. World Appl. Sci. J. 13(11), 2385–2388 (2011)
Shah, T., Hussain, I., Gondal, M.A., Khan, W.A.: Construction of cryptographically strong 8×8 S-boxes. World Appl. Sci. J. 13(11), 2389–2395 (2011)
Hussain, I., Shah, T., Gondal, M.A., Khan, M., Khan, W.A.: Construction of new S-box using a linear fractional transformation. World Appl. Sci. J. 14(12), 1779–1785 (2011)
Shah, T., Hussain, I., Gondal, M.A., Mahmood, H.: Statistical analysis of S-box in image encryption applications based on majority logic criterion. Int. J. Phys. Sci. 6(16), 4110–4127 (2011)
Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: Some analysis of S-box based on residue of prime number. Proc. Pak. Acad. Sci. 48(2), 111–115 (2011)
Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: Generalized majority logic criterion to analyze the statistical strength of S-boxes. Z. Naturforsch. 67a, 282–288 (2012)
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Hussain, I., Shah, T., Gondal, M.A. et al. A novel method for designing nonlinear component for block cipher based on TD-ERCS chaotic sequence. Nonlinear Dyn 73, 633–637 (2013). https://doi.org/10.1007/s11071-013-0816-9
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DOI: https://doi.org/10.1007/s11071-013-0816-9