Abstract
Self-inverse S-Boxes have been given much attention in the design of block ciphers recently. In this paper, based on Walsh Hadamard transform of Boolean functions, an evolutionary algorithm is investigated to increase the nonlinearity of self-inverse S-Boxes. The improved S-Boxes still remain self-inverse. Under this algorithm, randomly generated self-inverse S-Boxes can easily evolve into the ones with much higher nonlinearity.
This work was supported by Chinese Natural Science Foundation (Grant No.60373047 and 60025205) and 863 Project (Grant No. 2003AA14403).
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 subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Barreto, P.S.L.M., Rijmen, V.: The ANUBIS Block Cipher, http://planeta.terra.com.br/informatica/paulobarreto/AnubisPage.html
Chen, H., Feng, D.: An Effective Evolutionary Strategy for Bijective S-Boxes. In: Proceedings of the IEEE Congress on Evolutionary Computation 2004 (CEC 2004), Portland Oregon, June 20-23, pp. 2120–2123 (2004)
Chen, H., Feng, D., Wu, W.: An effective algorithm for improving the cryptographic properties of bijective S-Boxes. Journal of Computer Research and Development 41(8), 1410–1414 (2004)
Feng, D.-g., Wu, W.-l.: Designing And Analysis of Block Cipher, pp. 67–69. Tsinghua University Press, Beijing (2000)
Fuller, J., Millan, W., Dawson, E.: Multi-objective Optimisation of Bijective S-Boxes. In: Proceedings of the IEEE Congress on Evolutionary Computation 2004 (CEC 2004), Portland Oregon, June 20-23, pp. 1525–1532 (2004)
Kim, K., Matsumoto, T., Imai, H.: A Recursive Construction Method of S-Boxes Satisfying Strict Avalanche Criterion. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 564–574. Springer, Heidelberg (1991)
Millan, W., Burnett, L., Carter, G., Clark, A., Dawson, E.: Evolutionary Heuristics for Finding Cryptographically Strong S-Boxes. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 263–274. Springer, Heidelberg (1999)
Millan, W.: How to Improve the Nonlinearity of Bijective S-Boxes. In: Boyd, C., Dawson, E. (eds.) ACISP 1998. LNCS, vol. 1438, pp. 181–192. Springer, Heidelberg (1998)
Nyberg, K.: Perfect Nonlinear S-Boxes. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 378–386. Springer, Heidelberg (1991)
Nyberg, K.: On the Construction of Highly Nonlinear Permutations. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 92–98. Springer, Heidelberg (1993)
Pieprzyk, J.: Non-linearity of Exponent Permutations. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 81–92. Springer, Heidelberg (1990)
Pieprzyk, J.: Bent Permutations. In: International Conference on Finite Fields, Coding Theory and Advances in Communications, Las Vegas, pp. 173–181 (1991)
Pieprzyk, J., Finkelstein, G.: Permutations that Maximise Non-Linearity and their Cryptographic Significance. In: Proceedings of Fifth IFIP International Conference on Computer Security IFIP/SEC 1988, pp. 63–74 (1988)
Pieprzyk, J., Finkelstein, G.: Towards Effective Nonlinear Cryptosystem Design. IEE Proceedings, Pt E. 135(6), 325–335 (1988)
Webster, A.F., Tavares, S.E.: On the Design of S-Boxes. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 523–534. Springer, Heidelberg (1986)
Seberry, J., Zhang, X.-M., Zheng, Y.: Systematic Generation of Cryptographically Robust S-Boxes. In: Proceedings of the First ACM Conference on Computer and Communications Security, pp. 171–182 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, H., Feng, D. (2005). An Evolutionary Algorithm to Improve the Nonlinearity of Self-inverse S-Boxes. In: Park, Cs., Chee, S. (eds) Information Security and Cryptology – ICISC 2004. ICISC 2004. Lecture Notes in Computer Science, vol 3506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496618_26
Download citation
DOI: https://doi.org/10.1007/11496618_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26226-8
Online ISBN: 978-3-540-32083-8
eBook Packages: Computer ScienceComputer Science (R0)