Polynomial Selection for the Number Field Sieve Integer Factorisation Algorithm

Abstract

In this thesis we outline new research in integer factorisation with applications to public-key cryptography. In particular, we consider the number field sieve, the newest and fastest knownmethod for factorising integers used in public-key cryptosystems. We improve so-called polynomial selection methods for the number field sieve. Polynomial selection has been a major open problem for the number field sieve since its inception. We address the problem by modelling polynomial yield, and giving methods for finding polynomials with good yield. The improvements described here were used to obtain a new factorisation record, the 140 digit RSA modulus RSA-140, and are being used to obtain a further record by factorising a 512 bit RSA modulus RSA-155.