Topic
Ring of integers
About: Ring of integers is a research topic. Over the lifetime, 1856 publications have been published within this topic receiving 15882 citations.
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TL;DR: In this article, it was shown that the ring of integers in a quadratic imaginary number field is a free rank one module over the associated order (1.2) of K( )/K( ∗).
26 citations
TL;DR: In this paper, the first arithmetic extension group ExtˆX1(F,G) was introduced, which is an extension by groups of analytic types of the usual extension groups attached to OX-modules F and G over an arithmetic scheme X.
26 citations
08 Dec 2019
TL;DR: This work shows that the ambient ring is not the ring of integers of a number field, but rather an order (a full rank subring) that enjoys worst-case hardness with respect to short-vector problems in invertible-ideal lattices of the order.
Abstract: We propose a generalization of the celebrated Ring Learning with Errors (RLWE) problem (Lyubashevsky, Peikert and Regev, Eurocrypt 2010, Eurocrypt 2013), wherein the ambient ring is not the ring of integers of a number field, but rather an order (a full rank subring). We show that our Order-LWE problem enjoys worst-case hardness with respect to short-vector problems in invertible-ideal lattices of the order.
26 citations
TL;DR: In this paper, the authors studied variants of the Erd˝os distance problem and the dot products problem in the setting of the integers modulo q, where q = p! is a power of an odd prime.
Abstract: We study variants of the Erd˝os distance problem and the dot products problem in the setting of the integers modulo q, where q = p ! is a power of an odd prime.
26 citations
26 citations