A note on the multiple-recursive matrix method for generating pseudorandom vectors

TL;DR

This paper proposes an efficient algorithm for finding primitive multiple-recursive matrix methods to generate pseudorandom vectors and introduces a tweak to improve their linear complexity.

Contribution

It introduces a new algorithm for constructing primitive multiple-recursive matrix methods and enhances their linear complexity with a novel tweak.

Findings

Developed an efficient algorithm for primitive methods

Improved linear complexity of pseudorandom vector generation

Provides practical tools for cryptographic applications

Abstract

The multiple-recursive matrix method for generating pseudorandom vectors was introduced by Niederreiter (Linear Algebra Appl. 192 (1993), 301-328). We propose an algorithm for finding an efficient primitive multiple-recursive matrix method. Moreover, for improving the linear complexity, we introduce a tweak on the contents of the primitive multiple-recursive matrix method.