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An Experimental Study of the BDD Approach for the Search LWE Problem

  • Rui XuEmail author
  • Sze Ling Yeo
  • Kazuhide Fukushima
  • Tsuyoshi Takagi
  • Hwajung Seo
  • Shinsaku Kiyomoto
  • Matt Henricksen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10355)

Abstract

The proved hardness of the Learning With Errors (LWE) problem, assuming the worst case intractability of classic lattice problems, has made it a standard building block in the recent design of lattice based cryptosystems. Nonetheless, a thorough understanding of the security of these schemes from the perspective of existing attacks remains an open problem. In this manuscript, we report our implementation of the Bounded Distance Decoding (BDD) approach for solving the search LWE problem. We implement a parallel version of the pruned enumeration method of the BDD strategy proposed by Liu and Nguyen.

In our implementation we use the embarrassingly parallel design so that the power of multi-cores can be fully utilized. We let each thread take a randomized basis and perform independent enumerations to find the solution instead of parallelizing the enumeration algorithm itself. Other optimizations include fine-tuning the BKZ block size, the enumeration bound and the pruning coefficients and the optimal dimension of the LWE problem. Experiments are done using the TU Darmstadt LWE challenge. Finally we compare our implementation with a recent parallel BDD implementation by Kirshanova et al. [18] and show that our implementation is more efficient.

Keywords

Learning With Errors Lattice based cryptography Security evaluation Bounded Distance Decoding 

Supplementary material

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Rui Xu
    • 1
    Email author
  • Sze Ling Yeo
    • 2
  • Kazuhide Fukushima
    • 1
  • Tsuyoshi Takagi
    • 3
  • Hwajung Seo
    • 2
  • Shinsaku Kiyomoto
    • 1
  • Matt Henricksen
    • 4
  1. 1.KDDi Research Inc.FujiminoJapan
  2. 2.Institute for Infocomm Research (I2R)SingaporeSingapore
  3. 3.Institute of Mathematics for Industry (IMI)Kyushu UniversityFukuokaJapan
  4. 4.Huawei TechnologiesSingaporeSingapore

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