Affine equivalence of quartic homogeneous rotation symmetric Boolean functions

Homogeneous rotation symmetric Boolean functions have been extensively studied in recent years because of their applications in cryptography. Little is known about the basic question of when two such functions in n variables are affine equivalent. The simplest case of quadratic rotation symmetric functions which are generated by cyclic permutations of the variables in a single monomial was only settled in 2009, and the first substantial progress on the much more complicated cubic case came in 2010. In this paper, we show that much of the work on the cubic case can be extended to the quartic case. We also prove an exact formula for the number and sizes of the affine equivalence classes when n is a prime.