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Lazy Modulus Switching for the BKW Algorithm on LWE

  • Martin R. Albrecht
  • Jean-Charles Faugère
  • Robert Fitzpatrick
  • Ludovic Perret
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8383)

Abstract

Some recent constructions based on LWE do not sample the secret uniformly at random but rather from some distribution which produces small entries. The most prominent of these is the binary-LWE problem where the secret vector is sampled from {0,1} ∗  or { − 1,0,1} ∗ . We present a variant of the BKW algorithm for binary-LWE and other small secret variants and show that this variant reduces the complexity for solving binary-LWE. We also give estimates for the cost of solving binary-LWE instances in this setting and demonstrate the advantage of this BKW variant over standard BKW and lattice reduction techniques applied to the SIS problem. Our variant can be seen as a combination of the BKW algorithm with a lazy variant of modulus switching which might be of independent interest.

Keywords

Full Version Lattice Reduction Homomorphic Encryption Modulus Reduction Unbounded Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Martin R. Albrecht
    • 1
  • Jean-Charles Faugère
    • 3
    • 2
    • 4
  • Robert Fitzpatrick
    • 5
  • Ludovic Perret
    • 2
    • 3
    • 4
  1. 1.Technical University of DenmarkDenmark
  2. 2.Sorbonne Universités, UPMC Univ Paris 06, POLSYS, UMR 7606, LIP6, F-75005ParisFrance
  3. 3.INRIA, Paris-Rocquencourt Center, POLSYS ProjectFrance
  4. 4.CNRS, UMR 7606, LIP6, F-75005ParisFrance
  5. 5.Information Security Group Royal HollowayUniversity of London EghamSurreyUnited Kingdom

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