The Capacity of Private Information Retrieval From Heterogeneous Uncoded Caching Databases

Banawan, Karim; Arasli, Batuhan; Wei, Yi-Peng; Ulukuş, Şennur

doi:10.1109/tit.2020.2964762

Cited by 49 publications

(18 citation statements)

References 48 publications

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“…However, following the capacity characterization of PIR in [9], [10] under the assumption of long messages (where downloads dominate the communication cost), the fundamental limits (capacity) of various forms of download-efficient PIR have become an active topic in information theory. Recent advances include the capacity characterizations of PIR with T -privacy [11], symmetric-privacy [12], weak privacy [13], [14], eavesdroppers and/or Byzantine servers [15]- [19], coded storage [20]- [27], secure storage [28]- [30], limited storage [31]- [35], cached data or side information [36]- [39], multiple rounds [40], [41], multiple desired messages [42]- [45],…”

Section: Introductionmentioning

confidence: 99%

Double Blind T-Private Information Retrieval

Jia

Jafar

2021

IEEE J. Sel. Areas Inf. Theory

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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.

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Section: Introductionmentioning

confidence: 99%

Double Blind T-Private Information Retrieval

Jia

Jafar

2021

IEEE J. Sel. Areas Inf. Theory

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“…Server storage: Each server has the same storage capability and stores all K messages in the canonical model. The storage system at the servers has been generalized to MDS coded [11,12] or coded by a given linear code [13] for each message, and arbitrarily uncoded [14] with heterogeneous capabilities [15,16]. In these settings the iterative construction from [1] are still largely compatible with the storage structure.…”

Section: Introductionmentioning

confidence: 99%

Two-Level Private Information Retrieval

Zhou¹,

Tian²,

Sun³

et al. 2021

Preprint

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In the conventional robust T -colluding private information retrieval (PIR) system, the user needs to retrieve one of the possible messages while keeping the identity of the requested message private from any T colluding servers. Motivated by the possible heterogeneous privacy requirements for different messages, we consider the (N, T 1 : K 1 , T 2 : K 2 ) two-level PIR system, where K 1 messages need to be retrieved privately against T 1 colluding servers, and all the messages need to be retrieved privately against T 2 colluding servers where T 2 ≤ T 1 . We obtain a lower bound to the capacity by proposing two novel coding schemes, namely the non-uniform successive cancellation scheme and the non-uniform block cancellation scheme. A capacity upper bound is also derived. The gap between the upper bound and the lower bounds is analyzed, and shown to vanish when T 1 = T 2 . Lastly, we show that the upper bound is in general not tight by providing a stronger bound for a special setting.

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“…However, following the capacity characterization of PIR in [9], [10] under the assumption of long messages (where downloads dominate the communication cost), the fundamental limits (capacity) of various forms of downloadefficient PIR have become an active topic in information theory. Recent advances include the capacity characterizations of PIR with T -privacy [11], symmetric-privacy [12], weak privacy [13], [14], eavesdroppers and/or Byzantine servers [15]- [19], coded storage [20]- [27], secure storage [28]- [30], limited storage [31]- [35], cached data or side information [36]- [40], multiple rounds [41], [42], multiple desired messages [43]- [46], upload constraints [47], arbitrary collusion patterns [21], [48], as well as applications of PIR to private computation [49]- [52], private search [53], private set intersection [46], coded computing [54], locally decodable codes [55], etc.…”

Section: Introductionmentioning

confidence: 99%

Double Blind $T$-Private Information Retrieval

Lu,

Jia,

Jafar

2020

Preprint

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Double blind T -private information retrieval (DB-TPIR) enables two users, each of whom privately generates a random 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 messagessuch 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-XSTPIR) with multiple (M ) indices, each generated privately by 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.

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The Capacity of Private Information Retrieval From Heterogeneous Uncoded Caching Databases

Cited by 49 publications

References 48 publications

Double Blind T-Private Information Retrieval

Double Blind T-Private Information Retrieval

Two-Level Private Information Retrieval

Double Blind $T$-Private Information Retrieval

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