Efficient Linear Feedback Shift Registers with Maximal Period

We introduce and analyze an efficient family of linear feedback shift registers (LFSRʹs) with maximal period. This family is word-oriented and is suitable for implementation in software, thus provides a solution to a recent challenge [8]. The classical theory of LFSRʹs is extended to provide efficient algorithms for generation of irreducible and primitive LFSRʹs of this new type.