具有任意隐私要求的私有信息检索：介绍与容量结果
Private Information Retrieval With Arbitrary Privacy Requirements: Introduction and Capacity Results
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中文总结 AI 辅助
本文提出任意隐私要求下的私有信息检索问题，在基于图的存储系统中推导容量界限，并引入金字塔存储图以建模服务器存储。
中文摘要 AI 辅助
在本文中，我们提出了在基于图的存储系统中，在任意隐私要求下的私有信息检索（PIR）问题。这一问题的提出源于服务器存储限制、数据（消息）的丰富性以及异构数据隐私要求。在任意隐私要求下，每条消息必须从预先指定的服务器子集中私有地检索，该子集始终包含存储该消息的服务器。因此，每个服务器都与一个隐私集相关联，该隐私集预先指定了应从中私有检索的消息索引。该设置是经典PIR设置的推广，在经典PIR中，所需的消息索引需要对所有服务器保密，即每个服务器的隐私集包含所有消息索引。我们的设置也是新提出的本地PIR（LPIR）设置与经典PIR设置之间的桥梁，在前者中，隐私集恰好是存储的消息索引集。在本文中，我们在某些隐私要求下，针对一般图推导了PIR容量的通用下界和上界，这些界限捕捉了LPIR和经典PIR的本质。然后，我们关注路径和循环存储图在这些以及更细粒度设置下的情况，针对某些情况推导了容量结果，并为其他情况建立了上下界。它们的低度数使得能够更深入地理解新的隐私表述，并允许比其他简单图更多的隐私要求设置。最后，我们引入了一种新的图结构——金字塔存储图，来对服务器存储进行建模。尽管该图从未在任何PIR背景下被文献研究过，但它在消息存储和复制模式方面具有很好的对称结构。
英文摘要
In this paper, we introduce the problem of private information retrieval (PIR) under arbitrary privacy requirements, in a graph-based storage system. This formulation is motivated by the server storage limitations, abundance of data (messages) and heterogeneous data privacy requirements. Under the arbitrary privacy requirement, each message has to be retrieved privately from a pre-specified subset of servers, where the subset always includes the servers storing it. Thus, each server is associated with a privacy set, which pre-specifies the message indices that should be privately retrieved from it. This setting is a generalization of the classical PIR setting, where the required message index needs to be kept private from all servers, i.e., there, the privacy set of each server comprises all message indices. Our setting is also a bridge between the newly formulated local PIR (LPIR) setting and the classical PIR setting, where in the former, the privacy set is exactly the set of stored message indices. In this paper, we derive general lower and upper bounds on the PIR capacity for general graphs, under certain privacy requirements, that capture the essence of both LPIR and classical PIR. Then, we focus on path and cyclic storage graphs under these and more fine-grained settings, for which we derive capacity results for certain cases, and establish lower and upper bounds for others. Their low degree allows for a more in-depth understanding of the new privacy formulation and admits more privacy requirement settings compared to other simple graphs. Finally, we introduce a new graph structure, the pyramid storage graph, to model server storage. Although this graph has never been investigated in the literature in any PIR context, it enjoys a nice symmetric structure for message storage and replication patterns.
发表机构
- University of Maryland, College Park（马里兰大学帕克分校）
机构由 AI 辅助整理，请以论文原文为准。
