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Mathematics of Computation

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Quadratic sieving


Author: Thorsten Kleinjung
Journal: Math. Comp. 85 (2016), 1861-1873
MSC (2010): Primary 11Y05, 11Y16
DOI: https://doi.org/10.1090/mcom/3058
Published electronically: December 7, 2015
MathSciNet review: 3471111
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Abstract: We propose an efficient variant for the initialisation step of quadratic sieving, the sieving step of the quadratic sieve and its variants, which is also used in sieving-based algorithms for computing class groups of quadratic fields. As an application we computed the class groups of imaginary quadratic fields with 100-, 110-, 120-, and 130-digit discriminants.


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Additional Information

Thorsten Kleinjung
Affiliation: Laboratory for Cryptologic Algorithms, Station 14, EPFL, CH-1015 Lausanne, Swit- zerland

DOI: https://doi.org/10.1090/mcom/3058
Received by editor(s): November 21, 2013
Received by editor(s) in revised form: January 6, 2015
Published electronically: December 7, 2015
Article copyright: © Copyright 2015 American Mathematical Society