Root optimization of polynomials in the number field sieve

TL;DR

This paper presents algorithms for selecting polynomials with optimal root properties to improve the efficiency of the number field sieve in factoring large integers.

Contribution

It introduces new algorithms specifically designed to optimize the root properties of polynomials used in the GNFS.

Findings

Algorithms achieve better root properties in polynomial selection

Improved polynomial quality leads to more efficient factorization

Enhances the overall performance of the number field sieve

Abstract

The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some algorithms for selecting polynomials with very good root properties.