Families of rotation symmetric functions with useful cryptographic properties

It is known that the set of rotation symmetric Boolean functions has many functions with various useful properties for cryptography. This study shows how to construct some families of rotation symmetric functions which are balanced or plateaued. The authors also consider vectorial Boolean functions [that is, maps from GF(2)ⁿ to GF(2)^m] which are k-rotation symmetric and they give two infinite families of such functions which are permutations with the maximum possible algebraic degree. The families of functions that they give provide a source, which can be searched for functions with other useful cryptographic properties.