Ring-LWE密码
Ring-LWE Cryptography for the Number Theorist
摘要：
在本文中，我们调查的状态攻击环和多项式学习错误的问题（RLWE和PLWE）。最近的工作的安全性，这些问题[Eschenträger-Hallgren-Lauter，Elias-Lauter-Ozman-Stange]引起了有趣的问题，一些领域。我们扩展这些攻击和调查相关的开放问题，在数论中，包括频谱失真的代数数和它的关系，马勒措施，单演性质的整数环的数域，和大小的小阶模q的元素。
英文摘要：
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 [Eisenträger-Hallgren-Lauter, Elias-Lauter-Ozman-Stange] 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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