Private Proximity Retrieval Codes

Abstract

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 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 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.

Multi-Server Weakly-Private Information Retrieval

“…Note that this is also the optimized time-sharing Scheme 1 under the MaxL metric for (M, n) = (2, 2), where the optimal solution for ( 18) is (z * 0 , z * 1 ) = (2 − D, D − 1). The converse part is proven by (27), which gives…”

“…The case of maximum distance separable (MDS) coded servers was considered in [11], [12], while the case of arbitrary linear coded servers was studied in [13]- [15]. The concept of PIR has also been extended to several other relevant scenarios, which include colluding servers [11], [13], [15]- [19], robust PIR [16], PIR with Byzantine servers [20], optimal upload cost of PIR, i.e., the minimum required amount of query information [21], access complexity of PIR, i.e., the number of symbols accessed across all servers for the retrieval of a single file [22], single-server PIR with private side information [23], PIR on graph-based replication systems [24], PIR with secure storage [25], functional PIR codes [26], and private proximity retrieval codes [27].…”