🤖 AI Summary
本文通过提供一个从通用格版本到理想格问题的多项式时间归约，证明了在$\ell_2$范数下几个理想格问题（包括SVP和CVP）的最坏情况下的硬度。
📝 Abstract
We establish the worst-case hardness of several ideal lattice problems (including SVP and CVP) in the $\ell_2$ norm by providing a dimension-preserving, deterministic polynomial time reduction from their generic lattice versions. The reduction constructs an ideal lattice in the canonical embedding of a number field that approximates some input lattice up to scaling and orthogonal transformation. The integers defining the ideal and the ambient number ring, in particular its discriminant, are all polynomial in bit length relative to the generic input lattice. Furthermore, the ideal is invertible, the ring is monogenic, and the number field is totally real. If the number ring is also required to be a full ring of integers, the reduction conjecturally succeeds in bounded-error quantum polynomial time.