License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.19
URN: urn:nbn:de:0030-drops-66421
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6642/
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Stephens-Davidowitz, Noah

Search-to-Decision Reductions for Lattice Problems with Approximation Factors (Slightly) Greater Than One

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Abstract

We show the first dimension-preserving search-to-decision reductions for approximate SVP and CVP. In particular, for any gamma <= 1 + O(log n/n), we obtain an efficient dimension-preserving reduction from gamma^{O(n/log n)}-SVP to gamma-GapSVP and an efficient dimension-preserving reduction from gamma^{O(n)}-CVP to gamma-GapCVP. These results generalize the known equivalences of the search and decision versions of these problems in the exact case when gamma = 1. For SVP, we actually obtain something slightly stronger than a search-to-decision reduction - we reduce gamma^{O(n/log n)}-SVP to gamma-unique SVP, a potentially easier problem than gamma-GapSVP.

BibTeX - Entry

@InProceedings{stephensdavidowitz:LIPIcs:2016:6642,
  author =	{Noah Stephens-Davidowitz},
  title =	{{Search-to-Decision Reductions for Lattice Problems with Approximation Factors (Slightly) Greater Than One}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{19:1--19:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Klaus Jansen and Claire Mathieu and Jos{\'e} D. P. Rolim and Chris Umans},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6642},
  URN =		{urn:nbn:de:0030-drops-66421},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.19},
  annote =	{Keywords: Lattices, SVP, CVP}
}

Keywords: Lattices, SVP, CVP
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)
Issue Date: 2016
Date of publication: 06.09.2016

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