Wuhan Institute of Technology Network and Information Center
Polynomial selection is the first important step in number field sieve. A good polynomial not only can produce more relations in the sieving step, but also can reduce the matrix size. In this paper, the authors propose to use geometric view in the polynomial selection. In geometric view, the coefficients' interaction on size and the number of real roots are simultaneously considered in polynomial selection. They get two simple criteria. The first is that the leading coefficient should not be too large or some good polynomials will be omitted.