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LLL on the Average

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Algorithmic Number Theory (ANTS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 4076))

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Abstract

Despite their popularity, lattice reduction algorithms remain mysterious in many ways. It has been widely reported that they behave much more nicely than what was expected from the worst-case proved bounds, both in terms of the running time and the output quality. In this article, we investigate this puzzling statement by trying to model the average case of lattice reduction algorithms, starting with the celebrated Lenstra-Lenstra-Lovász algorithm (L3). We discuss what is meant by lattice reduction on the average, and we present extensive experiments on the average case behavior of L3, in order to give a clearer picture of the differences/similarities between the average and worst cases. Our work is intended to clarify the practical behavior of L3 and to raise theoretical questions on its average behavior.

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Author information

Authors and Affiliations

  1. CNRS & École normale supérieure, DI, 45 rue d’Ulm, 75005, Paris, France

    Phong Q. Nguyen

  2. LORIA / Université Nancy 1, 615 rue du J. Botanique, 54602, Villers-lès-Nancy, France

    Damien Stehlé

Authors
  1. Phong Q. Nguyen
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  2. Damien Stehlé
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Editor information

Editors and Affiliations

  1. Technische Universität Berlin, Germany

    Florian Hess

  2. Institut für Mathematik, MA 8–1, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Sebastian Pauli

  3. Institut für Mathematik, Technische Universität Berlin, Fakultät II, MA 8-1, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Michael Pohst

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© 2006 Springer-Verlag Berlin Heidelberg

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Nguyen, P.Q., Stehlé, D. (2006). LLL on the Average. In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_18

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  • DOI: https://doi.org/10.1007/11792086_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36075-9

  • Online ISBN: 978-3-540-36076-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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