The Capacity of Private Information Retrieval from Byzantine and Colluding Databases

Abstract

We consider the problem of single-round private information retrieval (PIR) from N replicated databases. We consider the case when B databases are outdated (unsynchronized), or even worse, adversarial (Byzantine), and therefore, can return incorrect answers. In the PIR problem with Byzantine databases (BPIR), a user wishes to retrieve a specific message from a set of M messages with zero-error, irrespective of the actions performed by the Byzantine databases. We consider the T -privacy constraint in this paper, where any T databases can collude, and exchange the queries submitted by the user. We derive the information-theoretic capacity of this problem, which is the maximum number of correct symbols that can be retrieved privately (under the Tprivacy constraint) for every symbol of the downloaded data. We determine the exact BPIR capacity to be C = N −2BThis capacity expression shows that the effect of Byzantine databases on the retrieval rate is equivalent to removing 2B databases from the system, with a penalty factor of N −2B N , which signifies that even though the number of databases needed for PIR is effectively N − 2B, the user still needs to access the entire N databases. The result shows that for the unsynchronized PIR problem, if the user does not have any knowledge about the fraction of the messages that are mis-synchronized, the single-round capacity is the same as the BPIR capacity. Our achievable scheme extends the optimal achievable scheme for the robust PIR (RPIR) problem to correct the errors introduced by the Byzantine databases as opposed to erasures in the RPIR problem. Our converse proof uses the idea of the cut-set bound in the network coding problem against adversarial nodes.

Capacity of Quantum Private Information Retrieval with Collusion of All But One of Servers

“…Several CPIR capacities have been derived (see Table I), e.g., the capacity when some servers may collude [13] and the capacity when the file set is coded and distributed to the servers [14]. Moreover, many other papers [15]- [22] have studied the CPIR capacity and the capacity-achieving protocols.…”

On the Information Leakage in Private Information Retrieval Systems

“…1:N , F), which is the amount of information that the user can obtain about the individual non-desired message-k ′ . The total leakage and the individual leakage in the systems are constrained as follows (12) where the parameters s and w are used to indicate the strong security requirement and the weak security requirement, respectively. For K = 2, since I(Wk; Q…”

Privacy-Preserving Smart Parking System Using Blockchain and Private Information Retrieval

“…This scheme is an information-theoretic PIR scheme for retrieving data from MDS-coded, colluding, unresponsive, and Byzantine databases. The reason we use this scheme instead of the capacity achieving scheme in [14] is to avoid the exponential file size (in the number of parking offers), which is needed to realize the scheme in [11]. Furthermore, as the number of parking offers become sufficiently large, the retrieval rate of [11] converges to the capacity expression of [14].…”

“…C [1] C [2] C [3] C [4] C [5] C [6] C [7] C [8] C [9] C [10] C [11] C [12] C [13] C [14] C [15] C [16] C [17] C [18] Figure 2: Nashville city, TN, USA is divided into geographical areas (cells).…”