Number Field Sieve with Provable Complexity

TL;DR

This paper explores the General Number Field Sieve, focusing on a modern randomized version with provable complexity, supported by extensive theoretical background in number theory and related fields.

Contribution

It introduces a randomized variant of the Number Field Sieve with proven complexity, advancing understanding of its theoretical foundations and practical implications.

Findings

Development of a randomized NFS with provable complexity

Integration of algebraic and analytic number theory techniques

Enhanced theoretical understanding of the algorithm's performance

Abstract

In this thesis we give an in-depth introduction to the General Number Field Sieve, as it was used by Buhler, Lenstra, and Pomerance, before looking at one of the modern developments of this algorithm: A randomized version with provable complexity. This version was posited in 2017 by Lee and Venkatesan and will be preceded by ample material from both algebraic and analytic number theory, Galois theory, and probability theory.