期刊名称：Facta universitatis - series: Electronics and Energetics
印刷版ISSN：0353-3670
电子版ISSN：2217-5997
出版年度：2018
卷号：31
期号：2
页码：189-205
DOI：10.2298/FUEE1802189S
出版社：University of Niš
摘要：Boolean functions expressing some particular properties often appear in engineering practice. Therefore, a lot of research efforts are put into exploring different approaches towards classification of Boolean functions with respect to various criteria that are typically selected to serve some specific needs of the intended applications. A classification is considered to be strong if there is a reasonably small number of different classes for a given number of variables n and it it desir able that classification rules are simple. A classification with respect to Walsh spectral coefficients, introduced formerly for digital system design purposes, appears to be useful in the context of Boolean functions used in cryptography, since it is in a way compatible with characterization of cryptographically interesting functions through Walsh spectral coefficients. This classification is performed in terms of certain spectral invariant operations. We show by introducing a new spectral invariant operation in the Walsh domain, that by starting from n≤5, some classes of Boolean functions can be merged which makes the classification stronger, and from the theoretical point of view resolves a problem raised already in seventies of the last century. Further, this new spectral invariant operation can be used in constructing bent functions from bent functions represented by quadratic forms. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. OI 174026]
