Ring-LWE Cryptography for the Number Theorist

Yara Elias; Kristin E.  Lauter; Ekin Ozman; Katherine E.  Stange

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 cryptography homomorphic 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: 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},
      url = {https://eprint.iacr.org/2015/758}
}