Better polynomials for GNFS

Bai, Shi; Bouvier, Cyril; Kruppa, Alexander; Zimmermann, Paul

doi:10.1090/mcom3048

Better polynomials for GNFS
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by Shi Bai, Cyril Bouvier, Alexander Kruppa and Paul Zimmermann;

Math. Comp. 85 (2016), 861-873

DOI: https://doi.org/10.1090/mcom3048

Published electronically: October 19, 2015

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Abstract:

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 selected polynomials can be modelled in terms of size and root properties. We propose a new kind of polynomial for GNFS: with a new degree of freedom, we further improve the size property. We demonstrate the efficiency of our 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.

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