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  Ring-LWE cryptography for the number theorist

Elias, Y., Lauter, K. E., Ozman, E., & Stange, K. E. (2016). Ring-LWE cryptography for the number theorist. In Directions in Number Theory: Proceedings of the 2014 WIN3 Workshop (pp. 271-290). Cham: Springer.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0004-6785-2 Version Permalink: https://hdl.handle.net/21.11116/0000-0004-6786-1
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 Creators:
Elias, Yara1, Author           
Lauter, Kristin E., Author
Ozman, Ekin, Author
Stange, Katherine E., Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory, Computer Science, Cryptography and Security
 Abstract: In this paper, we survey the status of attacks on the ring and polynomial learning with errors problems (RLWE and PLWE). Recent work on the security of these problems (Eisentraeger et al., Weak Instances of PLWE. In: Proceedings of the selected areas of cryptography 2014. Lecture notes in computer science. Springer,
New York, 2014; Elias Y., Lauter K., Ozman E., Stange K., Provably weak instances of ring-LWE. In: Advances in Cryptology – CRYPTO 2015. Springer, 2015 gives rise to interesting questions about number fields. We extend these attacks and survey related open problems in number theory, including spectral distortion of an algebraic number and its relationship to Mahler measure, the monogenic property for the ring of integers of a number field, and the size of elements of small order modulo q.

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Language(s): eng - English
 Dates: 2016
 Publication Status: Issued
 Pages: 20
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1508.01375
URI: http://arxiv.org/abs/1508.01375
DOI: 10.1007/978-3-319-30976-7_9
 Degree: -

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Title: Women in Numbers 3
Place of Event: Banff, Alberta
Start-/End Date: 2014-04-21 - 2014-04-25

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Title: Directions in Number Theory : Proceedings of the 2014 WIN3 Workshop
Source Genre: Proceedings
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Publ. Info: Cham : Springer
Pages: XV,339 S. Volume / Issue: - Sequence Number: - Start / End Page: 271 - 290 Identifier: ISBN: 978-3-319-30974-3
ISBN: 978-3-319-30976-7
DOI: 10.1007/978-3-319-30976-7

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Title: Association for Women in Mathematics Series
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Pages: - Volume / Issue: 3 Sequence Number: - Start / End Page: - Identifier: -