We consider a special case of $X$-secure $T$-private information retrieval (XSTPIR), where the security requirement is \emph{asymmetric} due to possible missing communication links between the $N$ databases considered in the system. We define the problem with a communication matrix that indicates all possible communications among the databases, and propose a database grouping mechanism that collects subsets of databases in an optimal manner, followed by a group-based PIR scheme to perform asymmetric XSTPIR with the goal of maximizing the communication rate (minimizing the download cost). We provide an upper bound on the general achievable rate of asymmetric XSTPIR, and show that the proposed scheme achieves this upper bound in some cases. The proposed approach outperforms classical XSTPIR under certain conditions, and the results of this work show that unlike in the symmetric case, some databases with certain properties can be dropped to achieve higher rates, concluding that more databases is not always better.

翻译：我们考虑 $X$-安全 $T$-私密信息检索（XSTPIR）的一个特例，其中由于系统中 $N$ 个数据库之间可能存在缺失的通信链路，安全要求是\emph{非对称}的。我们通过一个通信矩阵来定义该问题，该矩阵指示了数据库之间所有可能的通信关系，并提出了一种数据库分组机制，以最优方式收集数据库子集，随后采用基于分组的信息检索方案执行非对称 XSTPIR，目标是最大化通信速率（最小化下载开销）。我们给出了非对称 XSTPIR 一般可达速率的上界，并证明在某些情况下所提方案能达到该上界。所提方法在某些条件下优于经典 XSTPIR，且本研究结果表明，与对称情况不同，可以舍弃具有某些特性的数据库以获得更高速率，由此得出结论：并非数据库越多越好。