Parallel Streams of Nonlinear Congruential Pseudorandom Numbers

AbstractThis paper deals with the general nonlinear congruential method for generating uniform pseudorandom numbers, in which permutation polynomials over finite prime fields play an important role. It is known that these pseudorandom numbers exhibit an attractive equidistribution and statistical independence behavior. In the context of parallelized simulation methods, a large number of parallel streams of pseudorandom numbers with strong mutual statistical independence properties are required. In the present paper, such properties of parallelized nonlinear congruential generators are studied based on the discrepancy of certain point sets. Upper and lower bounds for the discrepancy both over the full period and over (sufficiently large) parts of the period are established. The method of proof rests on the classical Weil bound for exponential sums

Spectral analysis of random number generators

This paper is based on the theory developed by Dr. Evangelos Yfantis, professor of Computer Science at University of Nevada, Las Vegas. In this paper, we describe a method for testing the fairness of pseudorandom number generators using the Discrete Fourier Transform. We will show how the concept of a random process can be used in a representation for random discrete time signals. Using this concept, we have focused on the mathematical representations of the spectral analysis of a fair pseudorandom number generator. From this representation, a reasonable spectral expectation is determined. An algorithm which applies the developed method is described, and a modified shift register random number generator is used to produce sample data