Improved Reduction from the Bounded Distance Decoding Problem to the Unique Shortest Vector Problem in Lattices
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| Titel: | Improved Reduction from the Bounded Distance Decoding Problem to the Unique Shortest Vector Problem in Lattices |
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| Autoren: | Bai, Shi, Stehlé, Damien, Wen, Weiqiang |
| Weitere Verfasser: | Shi Bai and Damien Stehlé and Weiqiang Wen |
| Verlagsinformationen: | Schloss Dagstuhl – Leibniz-Zentrum für Informatik |
| Publikationsjahr: | 2016 |
| Bestand: | DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics ) |
| Schlagwörter: | Lattices, Bounded Distance Decoding Problem, Unique Shortest Vector Problem, Sparsification |
| Beschreibung: | 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. |
| Publikationsart: | article in journal/newspaper conference object |
| Dateibeschreibung: | application/pdf |
| Sprache: | 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 |
| Verfügbarkeit: | 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 |
| Dokumentencode: | edsbas.43D7B68B |
| Datenbank: | BASE |
Nájsť tento článok vo Web of Science | 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. |
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| DOI: | 10.4230/LIPIcs.ICALP.2016.76 |