Double blind T-private information retrieval

Abstract

Double blind T-private information retrieval (DB-TPIR) enables two users, each of whom specifies an index (θ1, θ2, resp.), to efficiently retrieve a message W(θ1, θ2) labeled by the two indices, from a set of N servers that store all messages W(k1, k2), k1 ∈ {1, 2, . . ., K1}, k2 ∈ {1, 2, . . ., K2}, such that the two users’ indices are kept private from any set of up to T1, T2 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 (T1, T2, . . ., TM), and arbitrary level of security (X) of data storage, so that the message W(θ1, θ2, . . ., θM) can be efficiently retrieved while the stored data is held secure against collusion among up to X colluding servers, the mth user’s index is private against collusion among up to Tm servers, and each user’s index θm is private from all other users. The general scheme relies on a tensor-product based extension of cross-subspace alignment and retrieves 1 - (X + T1 + · · · + TM)/N bits of desired message per bit of download.