On the distribution of some new explicit nonlinear congruential pseudorandom numbers

Abstract

Nonlinear methods are attractive alternatives to the linear congruential method for pseudorandom number generation. We introduce a new particularly attractive explicit nonlinear congruential method and present nontrivial results on the distribution of pseudorandom numbers generated by this method over the full period and in parts of the period. The proofs are based on new bounds on certain exponential sums over finite fields. © Springer-Verlag Berlin Heidelberg 2005.