Worst-case To Average-case Reductions Based On Gaussian Measure.pdf

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Preview of Worst-case to average-case reductions based on Gaussian measure
🔗 Source: cseweb.ucsd.edu
📊 Size: 522 KB
📄 Pages: 34 pages
⬇️ Downloads: 86

Summary

We show that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within a factor almost linear in the dimension of the lattice. The lattice problems considered are the shortest vector problem, the shortest independent vectors problem, the covering radius problem, and the guaranteed distance decoding problem. The approximation factor obtained is n logO(1) n for all four problems, greatly improving on previous work. Our results bring us closer to the limit where the problems are no longer known to be in NP intersect coNP.

Description

We show that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within...

Technical Information

  • File Format: PDF
  • File Size: 522 KB
  • Pages: 34
  • Language: EN
  • Total Downloads: 86
  • Last Updated: 4 weeks ago

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