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Full Lattice Basis Reduction on Graphics Cards

  • Timo Bartkewitz
  • Tim Güneysu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7242)

Abstract

Recent lattice enumeration GPU implementations are very useful to find shortest vectors within a given lattice but are also highly dependent on a lattice basis reduction that still runs on a CPU. Therefore we present an implementation of a full lattice basis reduction that makes exclusive use of GPUs to close this gap. Hence, we show that GPUs are, as well, suited to apply lattice basis reduction algorithms that were merely of theoretical interest so far due to their enormous computational effort. We modified and optimized these algorithms to fit the architecture of graphics cards, in particular we focused on Givens Rotations and the All-swap reduction method. Eventually, our GPU implementation achieved a significant speed-up for given lattice challenges compared to the NTL implementation running on an CPU of about 18, providing at least the same reduction quality.

Keywords

Lattice Basis Reduction Givens Rotations All-Swap Algorithm Parallelization Graphics Cards CUDA 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Timo Bartkewitz
    • 1
  • Tim Güneysu
    • 2
  1. 1.Department of Computer ScienceBonn-Rhine-Sieg University of Applied SciencesSankt AugustinGermany
  2. 2.Horst Görtz Institute for IT SecurityRuhr-University BochumGermany

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