Single-Server Multi-Message Private Information Retrieval with Side Information

We study the problem of single-server multi-message private information retrieval with side information. One user wants to recover $N$ out of $K$ independent messages which are stored at a single server. The user initially possesses a subset of $M$ messages as side information. The goal of the user is to download the $N$ demand messages while not leaking any information about the indices of these messages to the server. In this paper, we characterize the minimum number of required transmissions. We also present the optimal linear coding scheme which enables the user to download the demand messages and preserves the privacy of their indices. Moreover, we show that the trivial MDS coding scheme with $K-M$ transmissions is optimal if $N>M$ or $N^2+N \ge K-M$. This means if one wishes to privately download more than the square-root of the number of files in the database, then one must effectively download the full database (minus the side information), irrespective of the amount of side information one has available.Comment: 12 pages, submitted to the 56th Allerton conferenc

Double Blind TT-Private Information Retrieval

Double blind $T$-private information retrieval (DB-TPIR) enables two users, each of whom specifies an index ($\theta_1, \theta_2$, resp.), to efficiently retrieve a message $W(\theta_1,\theta_2)$ labeled by the two indices, from a set of $N$ servers that store all messages $W(k_1,k_2), k_1\in\{1,2,\cdots,K_1\}, k_2\in\{1,2,\cdots,K_2\}$, such that the two users' indices are kept private from any set of up to $T_1,T_2$ colluding servers, respectively, as well as from each other. A DB-TPIR scheme based on cross-subspace alignment is proposed in this paper, and shown to be capacity-achieving in the asymptotic setting of large number of messages and bounded latency. The scheme is then extended to $M$-way blind $X$-secure $T$-private information retrieval (MB-XS-TPIR) with multiple ($M$) indices, each belonging to a different user, arbitrary privacy levels for each index ($T_1, T_2,\cdots, T_M$), and arbitrary level of security ($X$) of data storage, so that the message $W(\theta_1,\theta_2,\cdots, \theta_M)$ can be efficiently retrieved while the stored data is held secure against collusion among up to $X$ colluding servers, the $m^{th}$ user's index is private against collusion among up to $T_m$ servers, and each user's index $\theta_m$ is private from all other users. The general scheme relies on a tensor-product based extension of cross-subspace alignment and retrieves $1-(X+T_1+\cdots+T_M)/N$ bits of desired message per bit of download.Comment: Accepted for publication in IEEE Journal on Selected Areas in Information Theory (JSAIT

Single-server Multi-user Private Information Retrieval with Side Information

In the problem of private information retrieval with side information, a single user wants to recover one of the K independent messages which are stored at one or multiple servers. The user initially has a subset of messages as side information. The goal of the user is to retrieve the demand message by using minimum number of transmissions (R∗) from the server(s) to the user under the condition that the index of the demand message should not be inferred by the server. We introduce the multi-user variant into this problem, where each user wants to retrieve one message and has a subset of messages as side information. In this paper, we study the special cases where all users want to retrieve one common message from a single server, but each user has different side information messages. We show that the optimal coding scheme can be constructed by first optimally partitioning the messages and then generating MDS codes separately in each subset of messages in the partition. We determine the R∗ , propose algorithms to compute R∗ , and construct optimal linear coding schemes with complexity polynomial in K (but exponential in the number of side information messages)