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Accelerating Lattice Reduction with FPGAs

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Progress in Cryptology – LATINCRYPT 2010 (LATINCRYPT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6212))

Abstract

We describe an FPGA accelerator for the Kannan–Fincke–Pohst enumeration algorithm (KFP) solving the Shortest Lattice Vector Problem (SVP). This is the first FPGA implementation of KFP specifically targeting cryptographically relevant dimensions. In order to optimize this implementation, we theoretically and experimentally study several facets of KFP, including its efficient parallelization and its underlying arithmetic. Our FPGA accelerator can be used for both solving stand-alone instances of SVP (within a hybrid CPU–FPGA compound) or myriads of smaller dimensional SVP instances arising in a BKZ-type algorithm. For devices of comparable costs, our FPGA implementation is faster than a multi-core CPU implementation by a factor around 2.12.

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Author information

Authors and Affiliations

  1. CARAMEL project-team, LORIA, INRIA / CNRS / Nancy Université, Campus Scientifique, BP 239, F-54506, Vandœuvre-lès-Nancy Cedex, France

    Jérémie Detrey

  2. Laboratoire LIP, CNRS-ENSL-INRIA-UCBL, ÉNS Lyon, Université de Lyon, 46 Allée d’Italie, 69364, Lyon Cedex 07, France

    Guillaume Hanrot & Xavier Pujol

  3. CNRS, Macquarie University and University of Sydney, Dpt. of Mathematics and Statistics, University of Sydney, NSW, 2006, Australia

    Damien Stehlé

Authors
  1. Jérémie Detrey
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  2. Guillaume Hanrot
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  3. Xavier Pujol
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  4. Damien Stehlé
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Editor information

Editors and Affiliations

  1. Computer Science Department, École Normale Supérieure, 45 Rue d’Ulm, 75230, Paris Cedex 05, France

    Michel Abdalla

  2. Computer Architecture and Networking Laboratory (LARC), Universidade de Sáo Paulo, Av. Prof. Luciano Gualberto, trav.3, n.158, 05508-900, Sáo Paulo (SP), Brazil

    Paulo S. L. M. Barreto

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Detrey, J., Hanrot, G., Pujol, X., Stehlé, D. (2010). Accelerating Lattice Reduction with FPGAs. In: Abdalla, M., Barreto, P.S.L.M. (eds) Progress in Cryptology – LATINCRYPT 2010. LATINCRYPT 2010. Lecture Notes in Computer Science, vol 6212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14712-8_8

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  • DOI: https://doi.org/10.1007/978-3-642-14712-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14711-1

  • Online ISBN: 978-3-642-14712-8

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