Trace representation of pseudorandom binary sequences derived from Euler quotients

TL;DR

This paper derives the trace representation of binary sequences from Euler quotients, enabling efficient sequence generation and analysis of cryptographic properties like linear complexity.

Contribution

It provides the explicit trace representation and defining polynomials for sequences derived from Euler quotients, which was not previously known.

Findings

Trace representation enables efficient sequence generation.

Analysis of cryptographic properties such as linear complexity.

Explicit defining polynomials for the sequences.

Abstract

We give the trace representation of a family of binary sequences derived from Euler quotients by determining the corresponding defining polynomials. Trace representation can help us producing the sequences efficiently and analyzing their cryptographic properties, such as linear complexity.