We study the private information retrieval (PIR) problem under arbitrary collusion patterns for replicated databases. We find its capacity, which is the same as the capacity of the original PIR problem with the number of databases $N$ replaced by a number $S^*$. The number $S^*$ is the optimal solution to a linear programming problem that is a function of the collusion pattern. Hence, the collusion pattern affects the capacity of the PIR problem only through the number $S^*$.
Consider the problem of Private Information Retrieval (PIR) where a user wishes to retrieve a single message from $N$ non-communicating and non-colluding databases (servers). All servers store the same set of $M$ messages and they respond to the user through a block fading Gaussian Multiple Access Channel (MAC). The goal in this setting is to keep the index of the required message private from the servers while minimizing the overall communication overhead. This work provides joint privacy-channel coding retrieval schemes for the AWGN MAC with and without fading. The schemes exploit the linearity of the channel while using the Compute and Forward (CF) coding scheme. Consequently, single-user encoding and decoding are performed to retrieve the private message. The achievable retrieval rates are shown to outperform a separation-based scheme for which the retrieval and the channel coding are designed separately. Moreover, these rates are asymptotically optimal as the SNR grows and are up to a constant gap of $2$ bits per channel use for every SNR.
Weakly-private information retrieval (WPIR) is a variant of the private information retrieval problem in which a user wants to efficiently retrieve a file stored across a set of servers while tolerating some information leakage on the identity of the requested file to the servers. In this paper, we consider WPIR from a single-server database where the information leakage is measured in terms of the mutual information (MI) or maximal leakage (MaxL) privacy metrics. In particular, we establish a connection between the WPIR problem and rate-distortion theory, and fully characterize the optimal tradeoff between the download cost and the allowed information leakage under the MI and MaxL metrics, settling the single-server WPIR capacity.
In the classical private information retrieval (PIR) setup, a user wants to retrieve a file from a database or a distributed storage system (DSS) without revealing the file identity to the servers holding the data. In the quantum PIR (QPIR) setting, a user privately retrieves a classical file by downloading quantum systems from the servers. The QPIR problem has been treated by Song et al. in the case of replicated servers, both without collusion and with all but one servers colluding. In this paper, the QPIR setting is extended to account for maximum distance separable (MDS) coded servers. The proposed protocol works for any [n,k]-MDS code and t-collusion with t=n-k. Similarly to the previous cases, the rates achieved are better than those known or conjectured in the classical counterparts.
A new computational private information retrieval (PIR) scheme based on random linear codes is presented. A matrix of messages from a McEliece scheme is used to query the server with carefully chosen errors. The server responds with the sum of the scalar multiple of the rows of the query matrix and the files. The user recovers the desired file by erasure decoding the response. Contrary to code-based cryptographic systems, the scheme presented here enables to use truly random codes, not only codes disguised as such. Further, we show the relation to the so-called error subspace search problem and quotient error search problem, which we assume to be difficult, and show that the scheme is secure against attacks based on solving these problems.