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Mathematics of Computation

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Applying sieving to the computation of quadratic class groups

Author: Michael J. Jacobson Jr.
Journal: Math. Comp. 68 (1999), 859-867
MSC (1991): Primary 11Y40; Secondary 11Y16
MathSciNet review: 1604324
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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

Keywords: Quadratic order, class group, sieving
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
Article copyright: © Copyright 1999 American Mathematical Society