Cryptology ePrint Archive: Report 2015/758

Ring-LWE Cryptography for the Number Theorist

Yara Elias and Kristin E. Lauter and 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.

Category / Keywords: public-key cryptography / lattice-based cryptography; homomorphic encryption

Date: received 29 Jul 2015, last revised 4 Sep 2015

Contact author: klauter at microsoft com

Available format(s): PDF | BibTeX Citation

Note: minor edits, references added

Version: 20150904:235426 (All versions of this report)

Short URL: ia.cr/2015/758

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