论文标题
关于正式单模型构造的保密增益$ \ text {a} _4 $ lattices
On the Secrecy Gain of Formally Unimodular Construction $\text{A}_4$ Lattices
论文作者
论文摘要
考虑了高斯窃听通道的晶格编码，目标是确保两个授权方之间可靠的通信，同时阻止窃听者学习传输的消息。最近，提出了一种称为保密增益的措施作为设计标准，以量化应用晶格代码的保密性。在本文中，theta系列的theta系列是由$ \ mathbb {z} _4 $的构造$ \ text {a} _4 $获得的正式形式的晶格，我们提供了一种通用方法，以确定他们的秘密收益。初始结果表明，构建$ \ text {a} _4 $ lattices可以比文献中最著名的单型晶格获得更高的保密增益。此外，提出了形式上自dual $ \ mathbb {z} _4 $ - 线性代码的新代码构建。
Lattice coding for the Gaussian wiretap channel is considered, where the goal is to ensure reliable communication between two authorized parties while preventing an eavesdropper from learning the transmitted messages. Recently, a measure called secrecy gain was proposed as a design criterion to quantify the secrecy-goodness of the applied lattice code. In this paper, the theta series of the so-called formally unimodular lattices obtained by Construction $\text{A}_4$ from codes over $\mathbb{Z}_4$ is derived, and we provide a universal approach to determine their secrecy gains. Initial results indicate that Construction $\text{A}_4$ lattices can achieve a higher secrecy gain than the best-known formally unimodular lattices from the literature. Furthermore, a new code construction of formally self-dual $\mathbb{Z}_4$-linear codes is presented.
