Using irreducible polynomials for random number generation

Abstract

A method is presented for generating random numbers with uniform distribution using linear recurrence sequences with very large period lengths. This method requires an irreducible polynomial modulo 2 to define the sequence. A suitable method for generating an infinite number of such polynomials is presented. The polynomials generated in this way can have an arbitrarily large degree, and a large enough order to make them suitable for practical applications.