A note on BDD problems with lambda 2 lambda 2-gap

In CRYPTO 2009, Lyubashevsky and Micciancio presented reductions BDD1/2 gamma BDD1/2 gamma (Bounded Distance Decoding Problem) [el] uSVP gamma uSVP gamma (Unique Shortest Vector Problem) [el] BDD1/ gamma BDD1/ gamma , and posed an open problem whether the reduction gap can be closed. This paper conc...

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Bibliographic Details
Published in:Information processing letters Vol. 114; no. 1-2; pp. 9 - 12
Main Authors: Liu, Mingjie, Wang, Xiaoyun, Xu, Guangwu, Zheng, Xuexin
Format: Journal Article
Language:English
Published: 01.02.2014
Subjects:
Data processing
Decoding
Lattices
Mathematical analysis
Reduction
Vectors (mathematics)
ISSN:0020-0190
Online Access:Get full text
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Summary:In CRYPTO 2009, Lyubashevsky and Micciancio presented reductions BDD1/2 gamma BDD1/2 gamma (Bounded Distance Decoding Problem) [el] uSVP gamma uSVP gamma (Unique Shortest Vector Problem) [el] BDD1/ gamma BDD1/ gamma , and posed an open problem whether the reduction gap can be closed. This paper concerns bounded distance decoding (BDD) problems for lattices with large lambda 2 lambda 2-gap. In the presence of larger lambda 2 lambda 2-gap, better reductions from BDD to uSVP and exact SVP are obtained. Some result can be regarded as a partial solution to the open problem.
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ISSN:0020-0190
DOI:10.1016/j.ipl.2013.10.004