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Construction of bent functions and balanced Boolean functions with high nonlinearity. (English) Zbl 0939.94563
Preneel, Bart (ed.), Fast software encryption. 2nd international workshop, Leuven, Belgium, December 14-16, 1994. Proceedings. Berlin: Springer-Verlag. Lect. Notes Comput. Sci. 1008, 61-74 (1995).
Summary: A general explicit construction of bent functions is described, which unifies well-known constructions due to Maiorana-McFarland and Dillon as two opposite extremal cases. Within this framework we also find new ways to generate bent functions. Then it is shown how the constructed bent functions can be modified in order to obtain highly nonlinear balanced Boolean functions. Although their nonlinearity is the best known so far, it remains open whether this bound can still be improved.
For the entire collection see [Zbl 0829.68005].

MSC:
94A60 Cryptography
06E30 Boolean functions
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