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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Root optimization of polynomials in the number field sieve
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by Shi Bai, Richard P. Brent and Emmanuel Thomé PDF
Math. Comp. 84 (2015), 2447-2457 Request permission

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 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.
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Additional Information
  • Shi Bai
  • Affiliation: Department of Mathematics, University of Auckland, Auckland, New Zealand.
  • Email: shih.bai@gmail.com
  • Richard P. Brent
  • Affiliation: Mathematical Sciences Institute, Australian National University, Australia.
  • Email: nfs@rpbrent.com
  • Emmanuel Thomé
  • Affiliation: INRIA Nancy, Villers-lès-Nancy, France.
  • Email: emmanuel.thome@inria.fr
  • Received by editor(s): June 14, 2013
  • Received by editor(s) in revised form: October 30, 2013, and December 7, 2013
  • Published electronically: February 11, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 2447-2457
  • MSC (2010): Primary 11Y05, 11Y16
  • DOI: https://doi.org/10.1090/S0025-5718-2015-02926-3
  • MathSciNet review: 3356034