Symmetric Private Information Retrieval with Mismatched Coded Messages and Randomness

Abstract

We consider the problem of symmetric private information retrieval (SPIR) with user-side common randomness. In SPIR, a user retrieves a message out of K messages from N non-colluding and replicated databases in such a way that no single database knows the retrieved message index (user privacy), and the user gets to know nothing further than the retrieved message (database privacy). SPIR has a capacity smaller than the PIR capacity which requires only user privacy, is infeasible in the case of a single database, and requires shared common randomness among the databases. We introduce a new variant of SPIR where the user is provided with a random subset of the shared database common randomness, which is unknown to the databases. We determine the exact capacity region of the triple (d, ρS, ρU ), where d is the download cost, ρS is the amount of shared database (server) common randomness, and ρU is the amount of available user-side common randomness. We show that with a suitable amount of ρU , this new SPIR achieves the capacity of conventional PIR. As a corollary, single-database SPIR becomes feasible. Further, the presence of user-side ρU reduces the amount of required server-side ρS.

Communication Cost of Two-Database Symmetric Private Information Retrieval: A Conditional Disclosure of Multiple Secrets Perspective

“…An achievable SPIR scheme is a scheme that satisfies the reliability constraint (6), the user privacy constraint (7) and the database privacy constraint (8). In this paper, we focus on the overall communication cost, which is a sum of the number of uploaded bits (named upload cost and denoted by U ) and the number of downloaded bits (named download cost and denoted by D), within the retrieval scheme.…”

Multi-User Blind Symmetric Private Information Retrieval from Coded Servers

“…are random noises that are used to guarantee T 1 = 2-private queries, and the coefficients α 4 , α 2 in Q (f1),1,1 i (α) and α 5 , α 3 in Q (f1),1,2 i (α) are used to separate the desired terms from the interference. This can be checked by expanding the answer polynomial A s (α) (46), as follows. In round s = 1,…”

“…In addition, each user must not learn any information about the other users' indices and the data files more than the desired one. The two constraints are called blind privacy and server privacy respectively, which are ensured by allowing all the servers to hold some correlated random variables that are independent of the files meanwhile unavailable to the users [30], [42], [44], [45], [46], and these variables are referred to as the randomness. The PIR problem with server privacy is called Symmetric PIR (SPIR).…”

“…1 The central technical contribution of this paper is an U-B-MDS-MB-XTSPIR scheme based on Lagrange encoding [52]. For the general setting of U-B-MDS-MB-XTSPIR, it may not be efficient to directly extend the current methods 1 Surprisingly, it is shown in [46], [44] that the retrieval rate 1 − K N of MDS-SPIR (Symmetric PIR with MDS coded storage) [42] can be further improved if the coded structure of the function outputs and randomness is mismatched, such as the function outputs are structured in MDS codes while the randomness is replicated. It is also a valuable research direction to explore how to use such mismatched randomness to lift the retrieval rate of the problems that include MDS-SPIR as a special case, for examples the problems in [19], [37], [44] and this paper.…”

Private Information Retrieval Schemes With Product-Matrix MBR Codes

“…[8]- [17]. Symmetric PIR schemes were considered in [18], [19]. Moreover, the capacity of [n, k]-MDS-coded PIR schemes was found by Banawan and Ulukus [10].…”