Root optimization of polynomials in the number field sieve
  The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some algorithms for selecting polynomials with very good root properties. 
Shi Bai, Richard P. Brent and Emmanuel Thom\'e
math.NT cs.DS