An Improvement to the Number Field Sieve

TL;DR

This paper presents an enhanced version of the number field sieve's sieving step, reducing its runtime significantly and providing theoretical proof of its efficiency under certain assumptions.

Contribution

It introduces a novel improvement to the sieving process in the number field sieve, achieving faster factoring and discrete logarithm computations.

Findings

Runtime is reduced to less than two-thirds of previous methods

Theoretical proof under certain assumptions confirms efficiency gains

Practical implications for cryptography and computational number theory

Abstract

We improve the "sieve" part of the number field sieve used in factoring integer and computing discrete logarithm. The runtime of our method is shorter than that of existing methods. Under some reasonable assumptions, we prove that it is less than two-thirds of the running time of the algorithm used before asymptotically with probability gr