On the concrete hardness of Learning with Errors

The learning with errors (LWE) problem has become a central building block of modern cryptographic constructions. This work collects and presents hardness results for concrete instances of LWE. In particular, we discuss algorithms proposed in the literature and give the expected resources required t...

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Bibliographic Details
Published inJournal of mathematical cryptology Vol. 9; no. 3; pp. 169 - 203
Main Authors Albrecht, Martin R., Player, Rachel, Scott, Sam
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.10.2015
Walter de Gruyter GmbH
Subjects
11T71
94A60
Algorithms
Applied mathematics
Concretes
Cryptography
Errors
Estimates
Hardness
lattice reduction
lattice-based cryptography
Lattices
Learning
Learning with Errors
Reduction
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Summary:The learning with errors (LWE) problem has become a central building block of modern cryptographic constructions. This work collects and presents hardness results for concrete instances of LWE. In particular, we discuss algorithms proposed in the literature and give the expected resources required to run them. We consider both generic instances of LWE as well as small secret variants. Since for several methods of solving LWE we require a lattice reduction step, we also review lattice reduction algorithms and use a refined model for estimating their running times. We also give concrete estimates for various families of LWE instances, provide a Sage module for computing these estimates and highlight gaps in the knowledge about algorithms for solving the LWE problem.
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ISSN:1862-2976
1862-2984
DOI:10.1515/jmc-2015-0016