The Inapproximability of Lattice and Coding Problems with Preprocessing

  • Authors:

  • Uriel Feige;Daniele Micciancio

  • Affiliations:

  • -;-

  • Venue:
  • CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
  • Year:
  • 2002

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Abstract

We prove that the closest vector problem with preprocessing (CVPP) is NP-hard to approximate within any factor less than sqrt(5/3). More specifically, we show that there exists a reduction from an NP-hard problem to the approximate closest vector problem such that the lattice depends only on the size of the original problem, and the specific instance is encoded solely in the target vector. It follows that there are lattices for which the closest vector problem cannot be approximated within factors gamma =1, showing that CVPP in the l_p norm is hard to approximate within any factor gamma