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.ICALP.2016.76
URN: urn:nbn:de:0030-drops-62085
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6208/
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Bai, Shi ; Stehlé, Damien ; Wen, Weiqiang

Improved Reduction from the Bounded Distance Decoding Problem to the Unique Shortest Vector Problem in Lattices

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Abstract

We present a probabilistic polynomial-time reduction from the lattice Bounded Distance Decoding (BDD) problem with parameter 1/( sqrt(2) * gamma) to the unique Shortest Vector Problem (uSVP) with parameter gamma for any gamma > 1 that is polynomial in the lattice dimension n. It improves the BDD to uSVP reductions of [Lyubashevsky and Micciancio, CRYPTO, 2009] and [Liu, Wang, Xu and Zheng, Inf. Process. Lett., 2014], which rely on Kannan's embedding technique. The main ingredient to the improvement is the use of Khot's lattice sparsification [Khot, FOCS, 2003] before resorting to Kannan's embedding, in order to boost the uSVP parameter.

BibTeX - Entry

@InProceedings{bai_et_al:LIPIcs:2016:6208,
  author =	{Shi Bai and Damien Stehl{\'e} and Weiqiang Wen},
  title =	{{Improved Reduction from the Bounded Distance Decoding Problem to the Unique Shortest Vector Problem in Lattices}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{76:1--76:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6208},
  URN =		{urn:nbn:de:0030-drops-62085},
  doi =		{10.4230/LIPIcs.ICALP.2016.76},
  annote =	{Keywords: Lattices, Bounded Distance Decoding Problem, Unique Shortest Vector Problem, Sparsification}
}

Keywords: Lattices, Bounded Distance Decoding Problem, Unique Shortest Vector Problem, Sparsification
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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