On the Average-Case Hardness of CVP

  • Authors:

  • J. Cai

  • Affiliations:

  • -

  • Venue:
  • FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
  • Year:
  • 2001

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Abstract

We prove a connection of the worst-case complexity to the average-case complexity based on the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP, with a non-trivial success probability, for lattices under a certain natural distribution, we show that one can approximately solve several lattice problems (including a version of CVP) efficiently for every lattice with high probability.