Algorithms for rotation symmetric Boolean functions

Abstract

Rotation Symmetric Boolean Functions (RSBFs) are of immense importance as building blocks of cryptosystems. This class of Boolean functions are invariant under circular translation of indices. It is known that, for n-variable RSBF functions, the associated set of all possible input n-bit strings can be divided into a number of subsets (called partitions or orbits), where every element (n-bit string) of a subset can be obtained by simply rotating the string of bits of some other element of the same subset. In this paper, for a given value of n, we propose algorithms for the generation of these partitions of all possible n-bit strings, each partition corresponding to a specific n-variable RSBF and its associated circular translations. These partitions can then be used to generate all possible n-variable RSBFs. The proposed algorithms are implemented for a maximum value of n = 41.