A multiple stream generator based on de Bruijn digraph homomorphisms

Abstract

We propose a method to obtain several streams of pseudorandom numbers based on a backbone generator of the generalized shift register type. The method is based on inverting one cycle in a de Bruijn digraph into many sequences in a higher-order de Bruijn graph via an appropriate graph homomorphism. We apply this technique to twisted generalized feedback shift register generators and to the Mersenne Twister MT19937. Positive results of statistical testing are reported.