Method for Generating Pseudorandom Sequence of Permutations Based on Linear Congruential Generator

Abstract

The results of the study of the graph of states of a linear congruential generator (LCG) are considered and theoretically substantiated. A model of a generalized graph of LCG states has been developed. It represents each connected component of the graph in the form of cycles equipped with tree products, allows classifying the types of connectivity components of the graph of LCG states and investigating the influence of parameters on its topology. A method for generating a pseudorandom sequence (PRS) of numbers based on the linear congruential method is presented. This method allows generating uniformly distributed numbers regardless of the topology of the graph of LCG states and, consequently, minimizing the time spent on choosing its parameters, and increasing the size of the space of their allowable values to achieve the maximum period. Computer implementation of the algorithm for generating PRS of permutations based on LCG with any type of graph of its states has allowed increasing the speed of the generator compared to the permutation generator using the modern Fisher-Yates algorithm.