Double Blind $T$-Private Information Retrieval
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866911151555608576 |
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| author | Lu, Yuxiang Jia, Zhuqing Jafar, Syed A. |
| author_facet | Lu, Yuxiang Jia, Zhuqing Jafar, Syed A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_03828 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Double Blind $T$-Private Information Retrieval Lu, Yuxiang Jia, Zhuqing Jafar, Syed A. Information Theory 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. |
| title | Double Blind $T$-Private Information Retrieval |
| topic | Information Theory |
| url | https://arxiv.org/abs/2008.03828 |