Paper 2015/758

Ring-LWE Cryptography for the Number Theorist

Yara Elias, Kristin E. Lauter, Ekin Ozman, and Katherine E. Stange

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 [EHL, ELOS] 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.

Note: minor edits, references added

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
lattice-based cryptographyhomomorphic encryption
Contact author(s)
klauter @ microsoft com
History
2015-09-04: last of 2 revisions
2015-07-30: received
See all versions
Short URL
https://ia.cr/2015/758
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2015/758,
      author = {Yara Elias and Kristin E.  Lauter and Ekin Ozman and Katherine E.  Stange},
      title = {Ring-LWE Cryptography for the Number Theorist},
      howpublished = {Cryptology ePrint Archive, Paper 2015/758},
      year = {2015},
      note = {\url{https://eprint.iacr.org/2015/758}},
      url = {https://eprint.iacr.org/2015/758}
}
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