Analysis of Statistical Properties of Nonlinear Feedforward Generators Over Finite Fields

TL;DR

This paper extends nonlinear feedforward logic to LFSRs over finite fields, analyzing their statistical properties and proposing a scheme that produces more balanced vector sequences than existing methods.

Contribution

It introduces a novel approach for applying nonlinear feedforward logic to word-based {\sigma}-LFSRs over finite fields, enhancing sequence balance.

Findings

Sequences are statistically more balanced with the proposed scheme.

Extension of nonlinear feedforward logic to arbitrary finite fields.

Improved statistical properties of generated sequences.

Abstract

Due to their simple construction, LFSRs are commonly used as building blocks in various random number generators. Nonlinear feedforward logic is incorporated in LFSRs to increase the linear complexity of the generated sequence. In this work, we extend the idea of nonlinear feedforward logic to LFSRs over arbitrary finite fields and analyze the statistical properties of the generated sequences. Further, we propose a method of applying nonlinear feedforward logic to word-based {\sigma}-LFSRs and show that the proposed scheme generates vector sequences that are statistically more balanced than those generated by an existing scheme.