Vector and parallel algorithms for integer factorisation

Abstract

The problem of finding the prime factors of large composite numbers is of practical importance since the advent of public key cryptosystems whose security depends on the presumed difficulty of this problem. In recent years the best known integer factorisation algorithms have improved greatly. It is now routine to factor 60-decimal digit numbers, and possible to factor numbers of more than 110 decimal digits. We describe several integer factorisation algorithms, and consider their suitability for implementation on vector processors and parallel machines.