Enumeration of Homogeneous Rotation Symmetric Functions over F_p

摘要

Rotation symmetric functions have been used as components of different cryptosystems. Functions in this class are invariant under circular translation of indices. In this paper, we will do some enumeration on homogeneous rotation symmetric functions over F_p. A formula for counting homogeneous rotation symmetric functions over F_p is presented when gcd(n, d) is a prime power, where n is the number of input variables and d is the algebraic degree of the function, which demonstrates that we solved one of the problems in [7].