Private Proximity Retrieval Codes (1907.10724v2)

Abstract: A \emph{private proximity retrieval} (\emph{PPR}) scheme is a protocol which allows a user to retrieve the identities of all records in a database that are within some distance $r$ from the user's record $x$. The user's \emph{privacy} at each server is given by the fraction of the record $x$ that is kept private. In this paper, this research is initiated and protocols that offer trade-offs between privacy and computational complexity and storage are studied. In particular, we assume that each server stores a copy of the database and study the required minimum number of servers by our protocol which provides a given privacy level. Each server gets a query in the protocol and the set of queries forms a code. We study the family of codes generated by the set of queries and in particular the minimum number of codewords in such a code which is the minimum number of servers required for the protocol. These codes are closely related to a family of codes known as \emph{covering designs}. We introduce several lower bounds on the sizes of such codes as well as several constructions. This work focuses on the case when the records are binary vectors together with the Hamming distance. Other metrics such as the Johnson metric are also investigated.