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

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Bibliographic Details
Title: Improved Reduction from the Bounded Distance Decoding Problem to the Unique Shortest Vector Problem in Lattices
Authors: Bai, Shi, Stehlé, Damien, Wen, Weiqiang
Contributors: Shi Bai and Damien Stehlé and Weiqiang Wen
Publisher Information: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Publication Year: 2016
Collection: DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics )
Subject Terms: Lattices, Bounded Distance Decoding Problem, Unique Shortest Vector Problem, Sparsification
Description: 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.
Document Type: article in journal/newspaper
conference object
File Description: application/pdf
Language: English
Relation: Is Part Of LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.76
DOI: 10.4230/LIPIcs.ICALP.2016.76
Availability: https://doi.org/10.4230/LIPIcs.ICALP.2016.76
https://nbn-resolving.org/urn:nbn:de:0030-drops-62085
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.76
Rights: https://creativecommons.org/licenses/by/3.0/legalcode
Accession Number: edsbas.43D7B68B
Database: BASE
Description
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.
DOI:10.4230/LIPIcs.ICALP.2016.76