Algorithms for Rotation Symmetric Boolean Functions

Abstract

Rotation Symmetric Boolean functions (RSBF) are of im- mense 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 in- put bit strings can be divided into a number of subsets (called partitions or orbits), where every element of a subset can be obtained by simply rotating the string of bits of some other element of the same subset. In this paper we propose algorithms for the generation of these partitions of RSBFs and implement for up to 26 variables.