Article ID Journal Published Year Pages File Type
6422679 Journal of Computational and Applied Mathematics 2014 7 Pages PDF
Abstract

The problem of counting Boolean functions with specified number s of Walsh coefficients ω in their Walsh spectrum is discussed in this paper. Strategies to solve this problem shall help solving many more problems related to desired cryptographic features of Boolean functions such as nonlinearity, resiliency, algebraic immunity, etc. In an attempt to study this problem, we present a new framework of solutions. We give results for |ω|≥2n−1 and for all s, in line with a previous work of Wu (1998) [12]. We also provide various results such as existence and construction for some s when ω=0, multiplicities for all ω and naive bounds on s for ω>2n/2.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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