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BY-NC-ND 3.0 license Open Access Published by De Gruyter October 2, 2015

On the concrete hardness of Learning with Errors

  • Martin R. Albrecht EMAIL logo , Rachel Player and Sam Scott


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.

MSC: 94A60; 11T71

Funding source: EPSRC

Award Identifier / Grant number: EP/L018543/1

Funding source: ACE-CSR PhD grant

Funding source: EPSRC

Award Identifier / Grant number: EP/K035584/1

We thank Steven Galbraith, Paul Kirchner and Cong Ling for pointing out mistakes and oversights in an earlier version of this work.

Received: 2015-3-19
Revised: 2015-9-20
Accepted: 2015-9-24
Published Online: 2015-10-2
Published in Print: 2015-10-1

© 2015 by De Gruyter

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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