标题： 语义私有信息检索与合谋服务器的容量 显示英文标题

标题： The Capacity of Semantic Private Information Retrieval with Colluding Servers

摘要： 我们研究了带有$T$个勾结服务器的语义私有信息检索（Sem-PIR）问题（Sem-TPIR），即共同分享用户查询的服务器。在Sem-TPIR中，消息大小不同，任何用户的消息检索概率不一致。这是经典PIR问题的推广，其中消息大小相等，消息检索概率相同。早期关于Sem-PIR的工作考虑了没有勾结的情况，即勾结参数为$T=1$。在本文中，我们考虑了任意$T < N$的一般问题。我们找到了检索率的上界，并设计了一个达到该率的方案，即推导出Sem-TPIR的精确容量。 显示英文摘要

摘要： We study the problem of semantic private information retrieval (Sem-PIR) with $T$ colluding servers (Sem-TPIR), i.e., servers that collectively share user queries. In Sem-TPIR, the message sizes are different, and message retrieval probabilities by any user are not uniform. This is a generalization of the classical PIR problem where the message sizes are equal and message retrieval probabilities are identical. The earlier work on Sem-PIR considered the case of no collusions, i.e., the collusion parameter of $T=1$. In this paper, we consider the general problem for arbitrary $T < N$. We find an upper bound on the retrieval rate and design a scheme that achieves this rate, i.e., we derive the exact capacity of Sem-TPIR.