Standard Generators of Finite Fields and their Cyclic Subgroups

TL;DR

This paper introduces standardized methods for constructing finite fields and their cyclic subgroup generators to facilitate consistent use across software and mathematical collections, serving as an alternative to Conway polynomials.

Contribution

It proposes standardized constructions and generators for finite fields and their cyclic subgroups, improving consistency and usability in computational and mathematical contexts.

Findings

Provides explicit standardized constructions for finite fields.

Defines standardized generators for cyclic subgroups in finite fields.

Aims to replace Conway polynomials in software and data collections.

Abstract

We define standardized constructions of finite fields, and standardized generators of (multiplicative) cyclic subgroups in these fields. The motivation is to provide a substitute for Conway polynomials which can be used by various software packages and in collections of mathematical data which involve finite fields.