# Period of K System Generator of Pseudorandom Numbers

## TL;DR

This paper analyzes the structure and period of pseudorandom number generators based on matrix systems, especially when related to Galois fields, providing explicit period calculations.

## Contribution

It offers a detailed analysis of the periodic trajectories of matrix-based pseudorandom generators and computes their periods using Galois field properties.

## Key findings

- Period of trajectories depends on prime p and matrix dimension d
- Structure becomes clearer when rational sublattice matches GF[p]
- Provides explicit formulas for trajectory periods

## Abstract

We analyze the structure of the periodic trajectories of the matrix generator of pseudorandom numbers which has been proposed earlier. The structure of the periodic trajectories becomes more transparent when the rational sublattice coincides with the Galois field $GF[p]$. We are able to compute the period of the trajectories as a function of $p$ and the dimension of the matrix $d$.