Bounds on the Capacity of Private Information Retrieval Over Graphs

Bar Sadeh, Yujie Gu*, Itzhak Tamo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In the private information retrieval (PIR) problem, a user wants to retrieve a file from a database without revealing any information about the desired file's identity to the servers that store the database. In this paper, we study the PIR capacity of a graph-based replication system, in which each file is stored on two distinct servers according to an underlying graph. This paper aims to provide upper and lower bounds to the PIR capacity of graphs via various graph properties. In particular, we provide several upper bounds on the PIR capacity that apply to all graphs. We further improve the bounds for specific graph families (which turn out to be tight in certain cases) by utilizing the underlying graph structure. For the lower bounds, we establish optimal rate PIR schemes for star graphs via edge-coloring techniques. Lastly, we provide an improved PIR scheme for complete graphs, implying an improved general lower bound on all graphs' PIR capacity.

Original languageEnglish
Pages (from-to)261-273
Number of pages13
JournalIEEE Transactions on Information Forensics and Security
Volume18
DOIs
StatePublished - 2023

Funding

FundersFunder number
Horizon 2020 Framework Programme852953
Japan Society for the Promotion of Science21K13830

    Keywords

    • Private information retrieval (PIR)
    • capacity
    • edge-coloring
    • graph-based replication system

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