Construction and enumeration of balanced rotation symmetric Boolean functions

Construction and enumeration of the class of balanced rotation symmetric Boolean functions are important research areas in cryptography. The counting results of this class of functions are available only for n=p, n=2p, and n=pq (where p and q are distinct primes). An explicit formula for counting balanced rotation symmetric Boolean functions for general n has been an open problem for the last few decades. This paper solves the above open problem using the concept of k-partition of multisets with equal sums. We extend this approach to construct and enumerate the balanced rotation symmetric functions over F_p.