The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
On the concrete hardness of Learning with Errors
Open accessAbstract
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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Cites
On lattices, learning with errors, random linear codes, and cryptography
Regev, O. (2009) · Journal of the ACM · doi:10.1145/1568318.1568324 · Cited by 2,315
Noise-tolerant learning, the parity problem, and the statistical query model
Blum, A., Kalai, A., & Wasserman, H. (2003) · Journal of the ACM · doi:10.1145/792538.792543 · Cited by 598
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A Full RNS Variant of Approximate Homomorphic Encryption
Cheon, J. H., Han, K., Kim, A., Kim, M., & Song, Y. (2019) · Lecture Notes in Computer Science · doi:10.1007/978-3-030-10970-7_16 · Cited by 357
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Marcolla, C., Sucasas, V., Manzano, M., Bassoli, R., Fitzek, F. H. P., & Aaraj, N. (2022) · Proceedings of the IEEE · doi:10.1109/jproc.2022.3205665 · Cited by 323
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Sav, S., Pyrgelis, A., Troncoso-Pastoriza, J. R., Froelicher, D., Bossuat, J.-P., Sousa, J. S., & Hubaux, J.-P. (2021) · Proceedings 2021 Network and Distributed System Security Symposium · doi:10.14722/ndss.2021.24119 · Cited by 162
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Esgin, M. F., Zhao, R. K., Steinfeld, R., Liu, J. K., & Liu, D. (2019) · Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security · doi:10.1145/3319535.3354200 · Cited by 96
Metadata
- Authors
- Albrecht, M. R., Player, R., & Scott, S.
- Venue
- Journal of Mathematical Cryptology
- Publisher
- Walter de Gruyter GmbH
- Published
- 2015-10-01
- Volume
- 9
- Issue
- 3
- Pages
- 169-203
- ISSN
- 1862-2976 (ISSN-L)
- 1862-2984
- OpenAlex
- W2400700555
- Cited by
- 861
- References
- 2
- FWCI
- 42.23
- Type
- journal article
- Language
- en
- Open access
- hybrid
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- Albrecht, M. R., Player, R., & Scott, S. (2015). On the concrete hardness of Learning with Errors. Journal of Mathematical Cryptology. https://doi.org/10.1515/jmc-2015-0016
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