AN IMPROVED SPECTRAL CLASSIFICATION OF BOOLEAN FUNCTIONS BASED ON AN EXTENDED SET OF INVARIANT OPERATIONS

Boolean functions expressing some particular properties often appear in engineering practice. Therefore, a lot of research efforts are put into exploring different approaches towards classi？cation of Boolean functions with respect to various criteria that are typically selected to serve some speci？c needs of the intended applications. A classi？cation 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 classi？cationrules are simple. A classi？cation with respect to Walsh spectral coef？cients, introduced formerly for digital system design purposes, appears to be useful in the context of Boolean functions used in cryptography, since it is ina way compatible with characterization of cryptographically interesting functions through Walsh spectral coef？cients. This classi？cation 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 classi？cation 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