Evolving Boolean Functions Satisfying Multiple Criteria
Many desirable properties have been identified for Boolean functions with cryptographic applications. Obtaining optimal tradeoffs among such properties is hard. In this paper we show how simulated annealing, a search technique inspired by the cooling processes of molten metals, can be used to derive functions with profiles of cryptographically-relevant properties as yet unachieved by any other technique.
KeywordsHeuristic Optimisation Boolean Functions Nonlinearity Autocorrelation Correlation Immunity
Unable to display preview. Download preview PDF.
- C. Carlet. On the coset weight divisibility and nonlinearity of resilient and correlation immune functions. In Sequences and Their Applications-SETA 2001, Discrete Mathematics and Theoretical Computer Science, pages 131–144. Springer Verlag, 2001.Google Scholar
- J.A. Clark and J. L. Jacob. Two-Stage Optimisation in the Design of Boolean Functions. In 5th Australasian Conference on Information, Security and Privacy-ACISP 2000, Lecture Notes in Computer Science, Volume 1841, pages 242–254. Springer-Verlag, 2000.Google Scholar
- H. Dobbertin. Construction of bent functions and balanced functions with high nonlinearity. In Fast Software Encryption, 1994 Leuven Workshop, Lecture Notes in Computer Science, Volume 1008, pages 61–74, Berlin, 1994. Springer-Verlag.Google Scholar
- T. Honda, T. Satoh, T. Iwata and K. Kurosawa. Balanced Boolean functions satisfying pc(2) and very large degree. Selected Areas in Cryptography (SAC) 1997. Available from http://adonis.ee.queensu.ca:8000/sac/sac97/papers.html
- S. Maitra. Highly nonlinear balanced Boolean functions with very good autocorrelation property. In Workshop on Coding and Cryptography-WCC 2001, Paris, January 8–12, 2001. Electronic Notes in Discrete Mathematics, Volume 6, Elsevier Science, 2001.Google Scholar
- W. Millan, A. Clark and E. Dawson. An effective genetic algorithm for finding highly nonlinear Boolean functions. In First International Conference on Information and Communications Security, Lecture Notes in Computer Science, Volume 1334, pages 149–158. Springer Verlag, 1997.Google Scholar
- W. Millan, A. Clark and E. Dawson. Boolean function design using hill climbing methods. In 4th Australasian Conference on Information, Security and Privacy, Lecture Notes in Computer Science, Volume 1587, pages 1–11. Springer Verlag, April 1999.Google Scholar
- E. Pasalic, S. Maitra, T. Johansson and P. Sarkar. New constructions of resilient and correlation immune Boolean functions achieving upper bound on nonlinearity. InWorkshop on Coding and Cryptography-WCC 2001, Paris, January 8–12, 2001. Electronic Notes in Discrete Mathematics, Volume 6, Elsevier Science, 2001.Google Scholar
- P. Sarkar and S. Maitra. Nonlinearity bounds and constuction of resilient Boolean functions. In Mihir Bellare, editor, Advances in Cryptology-Crypto 2000, Lecture Notes in Computer Science, Volume 1880, pages 515–532, Berlin, 2000. Springer-Verlag.Google Scholar
- Y. Tarannikov. On resilient Boolean fnctions with maximal possible nonlinearity. In Progress in Cryptology-INDOCRYPT 2000, Lecture Notes in Computer Science, Volume 1977, pages 19–30. Springer Verlag, 2000.Google Scholar
- Y.V. Tarannikov. New constructions of resilient Boolean functions with maximal nonlinearity. In Fast Software Encryption-FSE 2001, Lecture Notes in Computer Science, Volume 2355, pages 70–81. Springer Verlag, 2001.Google Scholar
- Y. Zheng and X. M. Zhang. Improved upper bound on the nonlinearity of high order correlation immune functions. In Selected Areas in Cryptography-SAC 2000, Lecture Notes in Computer Science, Volume 2012, pages 264–274. Springer Verlag, 2000.Google Scholar