Private Information Retrieval With Arbitrary Privacy Requirements: Introduction and Capacity Results
Researchers formulate private information retrieval under arbitrary graph-based privacy requirements, deriving capacity bounds and introducing pyramid storage graphs.
The paper generalizes classical private information retrieval (PIR) to arbitrary privacy requirements over graph-based storage systems, where each message is retrieved privately from a pre-specified server subset. The authors derive lower and upper capacity bounds for general graphs and exact capacity results for path and cyclic storage graphs. They also introduce a new pyramid storage graph structure that models symmetric message storage and replication patterns.
- Generalizes classical and local PIR via per-server privacy sets
- Capacity bounds derived for general, path, and cyclic storage graphs
- New pyramid storage graph models symmetric message replication
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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.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.15875