Double Blind T-Private Information Retrieval

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 messages W(k
₁
,k
₂
), k
₁
∈ {1,2,..., K
₁
}, k
₂
∈ {1,2,..., 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
,..., 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.