Strong Boolean Functions with Compact ANF Representation
Boolean functions are basic building blocks of virtually any cipher. Tremendous amount of research is devoted to finding Boolean functions that would be best suited for the job. A number of cryptographic criteria have been proposed that a Boolean function should fulfill to be considered for use in a cipher system. Most of these criteria in one way or another are correlated with function’s nonlinearity. Also a number of specific algebraic constructions and algorithms have been developed that allow us to obtain such Boolean functions with those desirable properties. Efficient representation and implementation of such cipher systems is another challenge faced by today’s cryptologists. This article presents a simple algorithm that is able to randomly generate Boolean functions with surprisingly good cryptographic properties, which at the same time have extremely short ANF representation, which could lead to efficient implementations.
KeywordsBoolean Function Truth Table Affine Function Bend Function Bent Function
Unable to display preview. Download preview PDF.
- J. A. Clark, J. L. Jacob, S. Stepney. Searching for cost functions. In CEC 2004: International Conference on Evolutionary Computation, Portland OR, USA, June 2004, pages 1517–1524, IEEE 2004.Google Scholar
- J. Fuller, W. Millan. On Linear Redundancy in the AES S-box. In Cryptology ePrint Archive, report 2002/111 , eprint.iacr.org, Aug 2002.Google Scholar
- J. Fuller, W. Millan. Linear Redundancy in S-Boxes. In T. Johansson, editor, February 24-26, 2003. Revised Papers, volume 2887 of Lecture Notes in Computer Science, pages 74–86, 2003.Google Scholar
- X. D. Hou. On the norm and covering radius of first-order Reed-Muller codes. In IEEE Transactions on Information Theory, 43(3):1025–1027, May 1997.Google Scholar
- J. A. Maiorana A Class of Bent Functions. In R41 Technical Paper, 1971.Google Scholar
- W. Meier, O. Staffelbach. Nonlinearity criteria for cryptographic functions. In J. J. Quisquater, J. Vandewalle, editors, Advances in Cryptology: EUROCRYPT 1989, pages 549–562, LNCS 434, Springer, 1989.Google Scholar
- W. Millan, A. Clark, E. Dawson. Heuristic design of cryptographically strong balanced Boolean functions. In Advances in Cryptology: EUROCRYPT 1998, pages 489–499, LNCS 1403, Springer, 1998.Google Scholar
- O. S. Rothaus. On bent functions. In Journal of Combinatorial Theory: Series A, 20:300–305, 1976.Google Scholar