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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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Applying sieving to the computation of quadratic class groups
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by Michael J. Jacobson Jr. PDF
Math. Comp. 68 (1999), 859-867 Request permission

Abstract:

We present a new algorithm for computing the ideal class group of an imaginary quadratic order which is based on the multiple polynomial version of the quadratic sieve factoring algorithm. Although no formal analysis is given, we conjecture that our algorithm has sub-exponential complexity, and computational experience shows that it is significantly faster in practice than existing algorithms.
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Additional Information
  • Michael J. Jacobson Jr.
  • Affiliation: Technische Universität Darmstadt, FB Informatik, Institut für theoretische Informatik, Alexanderstr. 10, 64283 Darmstadt, Germany
  • Email: jacobs@cdc.informatik.tu-darmstadt.de
  • Received by editor(s): May 5, 1997
  • Received by editor(s) in revised form: August 4, 1997
  • Additional Notes: The author is supported by the Natural Sciences and Engineering Research Council of Canada
  • © Copyright 1999 American Mathematical Society
  • Journal: Math. Comp. 68 (1999), 859-867
  • MSC (1991): Primary 11Y40; Secondary 11Y16
  • DOI: https://doi.org/10.1090/S0025-5718-99-01003-0
  • MathSciNet review: 1604324