On the structure of inversive pseudorandom number generators

Abstract

We analyze the lattice structure and linear complexity of a new inversive pseudorandom number generator recently introduced by Niederreiter and Rivat. In particular, we introduce a new lattice test which is much stronger than its predecessors and prove that this new generator passes it up to very high dimensions. Such a result cannot be obtained for the conventional inversive generator with currently known methods. We also analyze the behavior of two explicit inversive generators under this new test and present lower bounds on the linear complexity profile of binary sequences derived from these three inversive generators. © Springer-Verlag Berlin Heidelberg 2007.