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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| Published in | Journal of mathematical cryptology Vol. 9; no. 3; pp. 169 - 203 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin
De Gruyter
01.10.2015
Walter de Gruyter GmbH |
| Subjects | |
| Online Access | Get full text |
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| Abstract | 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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| AbstractList | 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. 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. |
| Author | Albrecht, Martin R. Scott, Sam Player, Rachel |
| Author_xml | – sequence: 1 givenname: Martin R. surname: Albrecht fullname: Albrecht, Martin R. email: martin.albrecht@rhul.ac.uk organization: Information Security Group, Royal Holloway, University of London, UK – sequence: 2 givenname: Rachel surname: Player fullname: Player, Rachel email: rachel.player.2013@live.rhul.ac.uk organization: Information Security Group, Royal Holloway, University of London, UK – sequence: 3 givenname: Sam surname: Scott fullname: Scott, Sam email: sam.scott.2012@live.rhul.ac.uk organization: Information Security Group, Royal Holloway, University of London, UK |
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| Snippet | The learning with errors (LWE) problem has become a central building block of modern cryptographic constructions. This work collects and presents hardness... |
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| SubjectTerms | 11T71 94A60 Algorithms Applied mathematics Concretes Cryptography Errors Estimates Hardness lattice reduction lattice-based cryptography Lattices Learning Learning with Errors Reduction |
| Title | On the concrete hardness of Learning with Errors |
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