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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Better polynomials for GNFS
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by Shi Bai, Cyril Bouvier, Alexander Kruppa and Paul Zimmermann PDF
Math. Comp. 85 (2016), 861-873 Request permission


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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Additional Information
  • Shi Bai
  • Affiliation: ENS de Lyon, Laboratoire LIP, (Université de Lyon, CNRS, ENSL, INRIA, UCBL), 69007 Lyon, France
  • Email:
  • Cyril Bouvier
  • Affiliation: INRIA Nancy - Grand Est, 54600 Villers-lès-Nancy, France
  • MR Author ID: 1075898
  • Email:
  • Alexander Kruppa
  • Affiliation: INRIA Nancy - Grand Est, 54600 Villers-lès-Nancy, France
  • Email:
  • Paul Zimmermann
  • Affiliation: INRIA Nancy - Grand Est, 54600 Villers-lès-Nancy, France
  • MR Author ID: 273776
  • Email:
  • Received by editor(s): June 18, 2013
  • Received by editor(s) in revised form: September 16, 2014
  • Published electronically: October 19, 2015
  • Additional Notes: The first author was supported in part by the ERC Starting Grant ERC-2013-StG-335086-LATTAC
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 85 (2016), 861-873
  • MSC (2010): Primary 11Y05, 11Y16
  • DOI:
  • MathSciNet review: 3434885