Section: New Results

Polynomial selection for the Number Field Sieve

Participants : Cyril Bouvier, Nicholas Coxon, Alexander Kruppa, Paul Zimmermann [contact] .

A new polynomial selection algorithm for GNFS (General Number Field Sieve) has been described in a preprint [24] and implemented in Cado-nfs . We demonstrate the efficiency of this algorithm by exhibiting a better polynomial than the one used for the factorization of RSA-768, and a polynomial for RSA-1024 that outperforms the best published one.

Montgomery's method of polynomial selection for GNFS has been analysed in a preprint [27] . Criteria for the selection of good parameters for Montgomery's method are given, and the existence of the modular geometric progressions used in the method is considered.