Cofactorisation strategies for the number field sieve and an estimate for the sieving step for factoring 1024-bit integers

The relation collection step for the number field sieve (NFS) is usually done by a combination of sieving techniques and methods for factoring the cofactors (cofactorisation). In this article a simplified model for the cofactorisation step is analysed and a method for finding good cofactorisation strategies is developed. This can be used to optimise hardware and software implementations. As an application we give an upper bound for the cost of the sieving step for a 1024-bit integer; using 12 million standard PCs it can be done within a year.