期刊
JOURNAL OF MATHEMATICAL CRYPTOLOGY
卷 9, 期 3, 页码 169-203出版社
WALTER DE GRUYTER GMBH
DOI: 10.1515/jmc-2015-0016
关键词
Learning with Errors; lattice-based cryptography; lattice reduction
资金
- EPSRC [EP/L018543/1, EP/K035584/1]
- ACE-CSR PhD grant
- EPSRC [EP/L018543/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/L018543/1] Funding Source: researchfish
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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