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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.

 

Selecting polynomials for the Function Field Sieve
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by Razvan Barbulescu PDF
Math. Comp. 84 (2015), 2987-3012 Request permission

Abstract:

The Function Field Sieve algorithm is dedicated to computing discrete logarithms in a finite field $\mathbb {F}_{q^n}$, where $q$ is a small prime power. The scope of this article is to select good polynomials for this algorithm by defining and measuring the size property and the so-called root and cancellation properties. In particular we present an algorithm for rapidly testing a large set of polynomials. Our study also explains the behaviour of inseparable polynomials, in particular we give an easy way to see that the algorithm encompass the Coppersmith algorithm as a particular case.
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Additional Information
  • Razvan Barbulescu
  • Affiliation: Université de Lorraine, CNRS, INRIA, France
  • Email: razvan.barbulescu@inria.fr
  • Received by editor(s): March 8, 2013
  • Received by editor(s) in revised form: October 18, 2013, and February 12, 2014
  • Published electronically: March 20, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 2987-3012
  • MSC (2010): Primary 12Y05; Secondary 12F15
  • DOI: https://doi.org/10.1090/S0025-5718-2015-02940-8
  • MathSciNet review: 3378859