Ring-LWE cryptography for the number theorist
arXiv preprint arXiv:1508.01375 |
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.