论文标题
双盲$ t $ - 私人信息检索
Double Blind $T$-Private Information Retrieval
论文作者
论文摘要
双盲$ t $ - 私人信息检索（DB-TPIR）使两个用户可以指定一个索引（$θ_1，θ_2$，resp。），以有效地检索消息$ W（θ_1，θ_2）$，由两个独立的$ N $ n $ n $ n $ n $ n $ n $ n $ N k_1 \ in \ {1,2，\ cdots，k_1 \}，k_2 \ in \ {1,2，\ cdots，k_2 \} $，使得两个用户的索引分别从任何设置的最高$ t_1，t_2，t_2 $ coldervers colleders colleders colluding colluding服务器中私有化。本文提出了基于跨空间对准的DB-TPIR方案，并在大量消息和有界延迟的渐近环境中表现出能量方面的成就。然后将该方案扩展到具有多个（$ m $）索引的$ M $ x $ x $ x $ x $ t $ t $ t $ - 私有信息检索（MB-xs-tpir），每个索引属于其他用户，每个索引的任意隐私级别（$ t_1，t_1，t_1，t_2，t_2，t_2，t_2，\ cdots，t_m $），以及$ x $ x $ x $ x $ x $ x $ x $ x $） $W(θ_1,θ_2,\cdots, θ_M)$ 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.一般方案依赖于基于张量产品的跨空间对齐的扩展，并检索$ 1-（x+t_1+\ cdots+t_m）/n $ n $ n $所需消息的位。
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 $W(k_1,k_2), k_1\in\{1,2,\cdots,K_1\}, k_2\in\{1,2,\cdots,K_2\}$, 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 $W(θ_1,θ_2,\cdots, θ_M)$ 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 $1-(X+T_1+\cdots+T_M)/N$ bits of desired message per bit of download.
