Applying sieving to the computation of quadratic class groups

Jacobson, Michael, Jr.

doi:10.1090/S0025-5718-99-01003-0

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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