Invariants of pseudo-random number generators

Pseudo-random number generators of the form Xn+i = P{xn), Vn = h{xn) are ubiquitous in applications ranging from cryptology to statistics. Such systems have been studied extensively in the control theory literature when Xn € K. In this paper we make a detailed study of the invariants of such systems when the underlying field is the Galois field of two elements. We consider various groups that act on such system.