Nonlinear Feedback Shift Registers and Zech Logarithms

TL;DR

This paper introduces a method to construct nonlinear feedback shift registers from linear ones using Zech logarithms, and proposes an algorithm to generate all de Bruijn sequences of a specified order.

Contribution

It presents a novel approach combining cross-join pairs and Zech logarithms to build nonlinear feedback shift registers and a hypothetical algorithm for de Bruijn sequence generation.

Findings

Constructed nonlinear feedback shift registers from linear ones.

Proposed a hypothetical algorithm for de Bruijn sequence generation.

Utilized Zech logarithms in finite fields for feedback function design.

Abstract

We construct feedback functions of Nonlinear Feedback Shift Registers from those of Linear Feedback Shift Registers using the cross-join pairs method and the Zech logarithms in finite fields. We present a hypothetical algorithm to generate all de Bruijn sequences of a given order.