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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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Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method
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by Antoine Joux and Reynald Lercier PDF
Math. Comp. 72 (2003), 953-967 Request permission

Abstract:

In this paper, we describe many improvements to the number field sieve. Our main contribution consists of a new way to compute individual logarithms with the number field sieve without solving a very large linear system for each logarithm. We show that, with these improvements, the number field sieve outperforms the gaussian integer method in the hundred digit range. We also illustrate our results by successfully computing discrete logarithms with GNFS in a large prime field.
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Additional Information
  • Antoine Joux
  • Affiliation: DCSSI, 18 rue du Dr. Zamenhoff, F-92131 Issy-les-Moulineaux, France
  • MR Author ID: 316495
  • Email: Antoine.Joux@m4x.org
  • Reynald Lercier
  • Affiliation: CELAR, Route de Laillé, F-35998 Rennes Armées, France
  • MR Author ID: 602270
  • ORCID: 0000-0002-0531-8945
  • Email: lercier@celar.fr
  • Received by editor(s): July 27, 1999
  • Received by editor(s) in revised form: October 18, 2000
  • Published electronically: November 4, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Math. Comp. 72 (2003), 953-967
  • MSC (2000): Primary 11T99; Secondary 11Y05
  • DOI: https://doi.org/10.1090/S0025-5718-02-01482-5
  • MathSciNet review: 1954978