Double Blind T-Private Information Retrieval

Abstract

Double blind T -private information retrieval (DB-TPIR) enables two users, each of whom specifies an index (θ 1 , θ 2 , resp.), to efficiently retrieve a message W (θ 1 , θ 2 ) labeled by the two indices, from a set of N servers that store all messagesthat 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 , • • • , T M ), and arbitrary level of security (X) of data storage, so that the message W (θ 1 , θ 2 , • • • , θ 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 θ 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 + • • • + T M )/N bits of desired message per bit of download.

Multi-User Blind Symmetric Private Information Retrieval from Coded Servers

“…As a result, this general scheme achieves a retrieval rate of 1 − K+X+T1+...+TM +2B−1 N −U with secrecy rate K+X+T1+...+TM −1 N −(K+X+T1+...+TM +2B+U−1) for any number of files, which generalizes the current optimal schemes as special cases of U-B-MDS-MB-XTSPIR including SPIR [30], MDS-SPIR [42], TSPIR [45], MDS-TSPIR [44], and MB-XTSPIR [24]. Further, when server privacy is not considered, the U-B-MDS-MB-XTSPIR scheme automatically yields the asymptotically optimal schemes for various special PIR cases as the number of files approaches infinity, for examples, U-B-MDS-TPIR [37], obtained by setting M = 1, X = 0, and U-B-MDS-XTPIR [19], obtained by setting M = 1.…”

“…The work that is most related to ours is [24] by Jafar et al, which introduces the problem of Multi-user Blind X-secure T -colluding Symmetric PIR, also referred to as MB-XTSPIR. Specifically, each file, labeled by M indices, is stored in an X-secure fashion at N servers, such that any group of up to X colluding servers learn nothing about the files.…”

“…Naturally, secrecy rate, defined as the amount of randomness relative to the desired file size, becomes another metric to measure the effectiveness of symmetric schemes. It is conceivable that such a functionality can be directly useful for collecting information cooperatively for multiple intelligence agencies and is useful for multi-way blind medical studies [24] where the confidential medical data are indexed by multiple attributes, such as the diagnosis, treatment, doctor, health insurance and so on. The multi-user blind functionality [24] is also directly useful for a variant of secure multiparty computation [49].…”

“…It is conceivable that such a functionality can be directly useful for collecting information cooperatively for multiple intelligence agencies and is useful for multi-way blind medical studies [24] where the confidential medical data are indexed by multiple attributes, such as the diagnosis, treatment, doctor, health insurance and so on. The multi-user blind functionality [24] is also directly useful for a variant of secure multiparty computation [49]. The M users/parties, each holds a private input (user m holds the input θ m for all m = 1, .…”

“…It is also a valuable research direction to explore how to use such mismatched randomness to lift the retrieval rate of the problems that include MDS-SPIR as a special case, for examples the problems in [19], [37], [44] and this paper. [16], [18], [19], [37], [24] to retrieve the desired file, please refer to Section IV for more explanation. To this end, we create a new form of interference alignment to PIR, which takes advantage of the structure inspired by the well-known Lagrange interpolation polynomials to construct storage codes and queries in privacy-preserving manners, such that the answers can be viewed as evaluations of polynomials and accordingly the decoding is completed by interpolating the polynomials.…”