New GNFS Polynomial Selection Paper Published
A new paper on polynomial selection in the General Number Field Sieve has been published[1]. The new method involves the creation of nonmonic linears. It is not expected to greatly increase the yield over Murphy’s method [2]. This code has been implemented in the pol5 code of Monico’s GGNFS.
[1] Kleinjund, T., On Polynomial Selection for the General Number Field Sieve, Mathematics of Computation, 75(256), 2006, pp 2037-2047.
Abstract:
The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present an improvement of the polynomial selection method of Montgomery and Murphy which has been used in recent GNFS records.
[2] Murphy, B. A., Brent, R. P. On Quadratic Polynomials for the Number Field Sieve, Computing Theory 98, ACSC 20(3), 1998, pp 199-215.