Abstract
In this work we focus on non-linearity and resiliency related criteria and explore a multi-objective evolutionary approach aiming to find balanced Boolean functions satisfying these criteria.We have shown that the multi-objective approach is better to apply than single objective optimization approaches. We have applied NSGA-II to find desired Boolean functions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Clark, J.A., Jacob, J.L., Stepney, S., Maitra, S., Millan, W.L.: Evolving Boolean Functions Satisfying Multiple Criteria. In: Menezes, A., Sarkar, P. (eds.) INDOCRYPT 2002. LNCS, vol. 2551, pp. 246–259. Springer, Heidelberg (2002)
Clark, J.A., Jacob, J.L.: Two-Sttage Optimization in the Design of Boolean Functions. In: Clark, A., Boyd, C., Dawson, E.P. (eds.) ACISP 2000. LNCS, vol. 1841, pp. 242–254. Springer, Heidelberg (2000)
Clark, J.A., Jacob, J.L., Stepney, S., Maitra, S., Millan, W.L.: Evolving Boolean Functions Satisfying Multiple Criteria. In: Menezes, A., Sarkar, P. (eds.) INDOCRYPT 2002. LNCS, vol. 2551, pp. 246–259. Springer, Heidelberg (2002)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm. IEEE Transection on Evolutionary Computation 6(2) (April 2002)
Aguirre, H., Okazaki, H., Fuwa, Y.: An Evolutionary Multiobjective Approach to Design Highly Non-linear Boolean Functions. In: GECCO 2007 (2007)
Maitra, S., Pasalic, E.: Further Constructions of Resilient Boolean Functions with Very High Nonlinearity. IEEE Transactions on Information Theory 48(7), 1825–1834 (2002)
Millan, W., Clark, A., Dawson, E.: An Effective Genetic Algorithm for Finding Highly Non-linear Boolean Functions. In: Han, Y., Quing, S. (eds.) ICICS 1997. LNCS, vol. 1334, pp. 149–158. Springer, Heidelberg (1997)
Millan, W., Clark, A., Dawson, E.: Heuristic Design of Cryptographically Strong Balanced Boolean Functions. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 489–499. Springer, Heidelberg (1998)
Millan, W., Clark, A., Dawson, E.: Boolean Function Design Using Hill Climbing Methods. In: Pieprzyk, J.P., Safavi-Naini, R., Seberry, J. (eds.) ACISP 1999. LNCS, vol. 1587, pp. 1–11. Springer, Heidelberg (1999)
Pasalic, E., Maitra, S., Johansson, T., Sarkar, P.: New Constructions of Resilient and Correlation Immune Boolean Functions Achieving Upper Bound on Nonlinearity. In: Proc. Workshop on Coding and Cryptography - WCC 2001, Electronic Notes in Discrete Mathematics, vol. 6. Elsevier Science (2001)
Sarkar, P., Maitra, S.: Nonlinearity Bounds and Constructions of Resilient Boolean Functions. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 515–532. Springer, Heidelberg (2000)
Srinivas, N., Kalyanmoy, D.: Multiobjective optimization Using Nondominating Sorting Genetic Algorithms. Massachusetts Institute of Technology Evolutionary Computation 2(3), 221–248
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer India Pvt. Ltd.
About this paper
Cite this paper
Goyal, R., Yadav, S.P., Kishor, A. (2012). Design of Boolean Functions Satisfying Multiple Criteria by NSGA-II. In: Deep, K., Nagar, A., Pant, M., Bansal, J. (eds) Proceedings of the International Conference on Soft Computing for Problem Solving (SocProS 2011) December 20-22, 2011. Advances in Intelligent and Soft Computing, vol 130. Springer, India. https://doi.org/10.1007/978-81-322-0487-9_45
Download citation
DOI: https://doi.org/10.1007/978-81-322-0487-9_45
Published:
Publisher Name: Springer, India
Print ISBN: 978-81-322-0486-2
Online ISBN: 978-81-322-0487-9
eBook Packages: EngineeringEngineering (R0)