Robust Private Information Retrieval Research Articles

Private Secure Coded Computation

We present private secure coded computation that ensures both the master’s privacy and data security against the workers, where the master aims to compute a function of its private data and a specific data in a library exclusively owned by the external workers. For privacy, the master should conceal the index of the specific data in the library against the workers. For security, the master should encrypt its private data. As an achievable scheme, we propose private secure polynomial codes and compare the proposed scheme with private polynomial codes in private coded computation and the optimal scheme of robust private information retrieval (RPIR).

The Capacity of Private Information Retrieval from Byzantine and Colluding Databases

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 We consider the case when B databases are outdated (unsynchronized), or even worse, adversarial (Byzantine), and therefore, can return incorrect answers.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 T-privacy constraint) for every symbol of the downloaded data. We determine the exact BPIR capacity to be C = (N -2B)/N·(1-T/(N-2B))/(1-(T/(N - 2B)) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sup> ), if 2B + T <; N. This 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 missynchronized, 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.

The Capacity of Robust Private Information Retrieval With Colluding Databases

Private information retrieval (PIR) is the problem of retrieving as efficiently as possible, one out of $K$ messages from $N$ non-communicating replicated databases (each holds all $K$ messages) while keeping the identity of the desired message index a secret from each individual database. The information theoretic capacity of PIR (equivalently, the reciprocal of minimum download cost) is the maximum number of bits of desired information that can be privately retrieved per bit of downloaded information. $T$-private PIR is a generalization of PIR to include the requirement that even if any $T$ of the $N$ databases collude, the identity of the retrieved message remains completely unknown to them. Robust PIR is another generalization that refers to the scenario where we have $M \geq N$ databases, out of which any $M - N$ may fail to respond. For $K$ messages and $M\geq N$ databases out of which at least some $N$ must respond, we show that the capacity of $T$-private and Robust PIR is $\left(1+T/N+T^2/N^2+\cdots+T^{K-1}/N^{K-1}\right)^{-1}$. The result includes as special cases the capacity of PIR without robustness ($M=N$) or $T$-privacy constraints ($T=1$).

Robust Information-Theoretic Private Information Retrieval

An information-theoretic private information retrieval (PIR) protocol allows a user to retrieve a data item of its choice from a database replicated amongst several servers, such that each server gains absolutely no information on the identity of the item being retrieved. One problem with this approach is that current systems do not guarantee availability of servers at all times for many reasons, e.g., crash of server or communication problems. In this work we design robust PIR protocols, i.e., protocols which still work correctly even if only some servers are available during the protocol's operation. We present various robust PIR protocols giving different tradeoffs between the different parameters. We first present a generic transformation from regular PIR protocols to robust PIR protocols. We then present two constructions of specific robust PIR protocols. Finally, we construct robust PIR protocols which can tolerate Byzantine servers, i.e., robust PIR protocols which still work in the presence of malicious servers or servers with a corrupted or obsolete database.

A Geometric Approach to Information-Theoretic Private Information Retrieval

A t-private private information retrieval (PIR) scheme allows a user to retrieve the ith bit of an n-bit string x replicated among k servers, while any coalition of up to t servers learns no information about i. We present a new geometric approach to PIR and obtain the following: (1) A t-private k-server protocol with communication $O (\frac{k^2}{t} \log k n^{1/\left \lfloor (2k-1)/t \right \rfloor})$, removing the ${k}{t}$ term of previous schemes. This answers an open question of [Y. Ishai and E. Kushilevitz, in Proceedings of the $31$st ACM Symposium on Theory of Computing, 1999, pp. 79–88]. (2) A 2-server protocol with $O(n^{1/3})$ communication, polynomial preprocessing, and online work $O(n/\log^r n)$ for any constant r. This improves the $O(n/\log^2 n)$ work of [A. Beimel, Y. Ishai, and T. Malkin, J. Cryptology, 17 (2004), pp. 125–151]. (3) Smaller communication for instance hiding [D. Beaver, J. Feigenbaum, J. Kilian, and P. Rogaway, J. Cryptology, 10 (1997), pp. 17–36; Y. Ishai and E. Kushilevitz, in Proceedings of the $31$st ACM Symposium on Theory of Computing, 1999, pp. 79–88], PIR with a polylogarithmic number of servers, and robust PIR [A. Beimel and Y. Stahl, in Proceedings of the 3rd Conference on Security in Communications Networks (SCN $2002$), Lecture Notes in Comput. Sci. 2576, Springer, Berlin, 2003, pp. 326–341].