Private Proximity Retrieval Codes

A private proximity retrieval (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 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, 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 receives a query in the protocol and the set of queries forms a code. The main focus in the paper is dedicated to studying the family of codes generated by the set of queries. These codes will be shown to satisfy a specific covering property and will be called private proximity retrieval intersection covering codes. In particular, since the query every server receives is a codeword, the goal is to minimize the number of codewords in such a code which is the minimum number of servers required by the protocol. These codes are closely related to a family of codes known as 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.