Inapproximability of the Shortest Vector Problem: Toward a Deterministic Reduction

@article{Micciancio2012InapproximabilityOT,
  title={Inapproximability of the Shortest Vector Problem: Toward a Deterministic Reduction},
  author={Daniele Micciancio},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2012},
  volume={19},
  pages={20}
}
We prove that the Shortest Vector Problem (SVP) on point lattices is NPhard to approximate for any constant factor under polynomial-time randomized reductions with one-sided error that produce no false positives. We also prove inapproximability for quasi-polynomial factors under the same kind of reductions running in subexponential time. Previous hardness results for SVP either incurred two-sided error, or only proved hardness for small constant approximation factors. Close similarities between… CONTINUE READING
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