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Factoring N = pq 2 with the Elliptic Curve Method

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Algorithmic Number Theory (ANTS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2369))

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Abstract

Various cryptosystems have been proposed whose security relies on the difficulty of factoring integers of the special form N = pq 2. To factor integers of that form, Peralta and Okamoto introduced a variation of Lenstra’s Elliptic Curve Method (ECM) of factorization, which is based on the fact that the Jacobi symbols (a/N) and (a/P) agree for all integers a coprime with q. We report on an implementation and extensive experiments with that variation, which have been conducted in order to determine the speed-up compared with ECM for numbers of general form.

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Author information

Authors and Affiliations

  1. Institut für Algorithmen und Kognitive Systeme, Universität Karlsruhe, Postfach 6980, 76128, Karlsruhe, Germany

    Peter Ebinger

  2. Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Edlyn Teske

Authors
  1. Peter Ebinger
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  2. Edlyn Teske
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Editor information

Editors and Affiliations

  1. School of Mathematics and Statistics, F07, University of Sydney, Sydney, NSW, 2006, Australia

    Claus Fieker  & David R. Kohel  & 

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© 2002 Springer-Verlag Berlin Heidelberg

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Ebinger, P., Teske, E. (2002). Factoring N = pq 2 with the Elliptic Curve Method. In: Fieker, C., Kohel, D.R. (eds) Algorithmic Number Theory. ANTS 2002. Lecture Notes in Computer Science, vol 2369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45455-1_37

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  • DOI: https://doi.org/10.1007/3-540-45455-1_37

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43863-2

  • Online ISBN: 978-3-540-45455-7

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