基于图的复制系统的本地私有信息检索

中文摘要 AI 辅助

我们重新思考了多服务器图复制私有信息检索（PIR）系统中的隐私定义，引入了一种新的设置：用户的隐私由服务器的存储结构决定。在经典的图复制PIR中，用户从服务器检索存储的单个消息，同时对每个服务器隐藏消息索引。在我们提出的隐私设置中，用户仅在特定服务器存储正在检索的消息时，才需要向该服务器隐藏消息索引，其他情况下不施加隐私要求。我们将这种放宽的隐私要求命名为本地用户隐私，将由此产生的PIR问题命名为图上的本地PIR。我们的研究重点是双复制PIR系统，其中每条消息被复制两次并存储在两个不同的服务器上。具体而言，我们研究存储由简单图（即每对顶点最多关联一条边）及其多重图扩展（即每条边替换为r条平行边）表示的本地PIR系统。针对这些设置，我们确定了本地PIR容量的边界，本地PIR容量定义为每下载一个符号所能检索的最大消息符号数。在相同存储结构下，本地隐私要求带来了比经典PIR容量显著的容量增益。例如，当图是多个相同子图的不交并时，本地PIR容量相对于经典PIR容量的增益是子图数量的乘积。此外，对于连通图，我们推导了边传递图和二分图的容量下界，该下界大于已知的最佳PIR容量边界。通过这些推导并建立匹配的上界，我们精确刻画了星形图、循环图和奇数个顶点的路径图的容量。我们为一般图引入了两种本地PIR方案。

英文摘要

We rethink the definition of privacy in multi-server, graph-replicated private information retrieval (PIR) systems, by introducing a novel setting where the user's privacy is governed by the servers' storage structure. In classical graph-replicated PIR, the user retrieves a single message stored at the servers, while hiding the message index from each server. In our proposed privacy setting, the user is concerned with hiding the message index from a particular server, only if that server stores the message being retrieved, and privacy is not imposed otherwise. We coin this relaxed privacy requirement as local user privacy and the resulting PIR problem as local PIR on the graph. Our focus is on two-replicated PIR systems, where every message is replicated twice and stored on two distinct servers. Specifically, we study local PIR systems where the storage is represented by simple graphs, i.e., every pair of vertices is associated with at most one edge, and by their multigraph extension, i.e., $r$ parallel edges replace every edge. For these settings, we establish bounds on the local PIR capacity, defined as the maximum number of message symbols retrieved, per downloaded symbol. The local privacy requirement yields significant capacity gain over the classical PIR capacity under the same storage structure. For instance, in settings where the graph is a disjoint union of multiple identical sub-graphs, the gain in the local PIR capacity over classical PIR capacity is multiplicative in the number of sub-graphs. Further, for connected graphs, we derive capacity lower bounds for edge-transitive and bipartite graphs, which are greater than the best-known PIR capacity bounds. From these and by establishing matching upper bounds, we exactly characterize the capacity for star graphs, cyclic graphs, and path graphs with odd number of vertices. We introduce two local PIR schemes for general graphs.

发表机构

• University of Maryland, College Park（马里兰大学帕克分校）

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