Fast K System Generators of Pseudorandom Numbers

TL;DR

This paper introduces a fast algorithm for matrix-based pseudorandom number generators using Kolmogorov-Anosov K systems, significantly reducing computation time and clarifying their algebraic structure.

Contribution

It presents a novel algorithm that reduces the complexity of K system generators from quadratic to near-linear time, improving efficiency and understanding.

Findings

Reduction of generation time from N^2 to N log N operations

Clarification of the algebraic structure of K system generators

Enhanced efficiency of pseudorandom number generation

Abstract

We suggest fast algorithm for the matrix generator of pseudorandom numbers based on Kolmogorov-Anosov K systems which has been proposed earlier. This algorithm reduces $N^{2}$ operation of the matrix generator to $NlnN$ and essentially reduces the generation time. It also clarifies the algebraic structure of this type of K system generators.