The Capacity of Multi-round Private Information Retrieval from Byzantine Databases

Yao, Xinyu; Liu, Nan; Kang, Wei

doi:10.1109/isit.2019.8849275

Cited by 13 publications

(5 citation statements)

References 24 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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“…However, the capacity for the natural setting of secure storage remains unknown, and relatively unexplored. While a number of efforts are motivated by security concerns, such efforts have focused largely on other models, e.g., wiretap models where data security is desired against eavesdroppers listening to the communication between the user and the servers [21,22], Byzantine models where the servers may respond incorrectly by introducing erasures or errors in their response to the user's queries [23][24][25][26][27], and so called symmetric security models [28][29][30] that allow the user to learn nothing about the data besides his desired message. An exception in this regard is the recent work in [31] where PIR with distributed storage is explored and the asymptotic (large K) capacity for the X = T = 1 setting is bounded as…”

Section: Introductionmentioning

confidence: 99%

Cross Subspace Alignment and the Asymptotic Capacity of $X$ -Secure $T$ -Private Information Retrieval

Jia

Sun

Jafar

2019

IEEE Trans. Inform. Theory

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X-secure and T -private information retrieval (XSTPIR) is a form of private information retrieval where data security is guaranteed against collusion among up to X servers and the user's privacy is guaranteed against collusion among up to T servers. The capacity of XSTPIR is characterized for arbitrary number of servers N , and arbitrary security and privacy thresholds X and T , in the limit as the number of messages K → ∞. Capacity is also characterized for any number of messages if either N = 3, X = T = 1 or if N ≤ X + T . Insights are drawn from these results, about aligning versus decoding noise, dependence of PIR rate on field size, and robustness to symmetric security constraints. In particular, the idea of cross subspace alignment, i.e., introducing a subspace dependence between Reed-Solomon code parameters, emerges as the optimal way to align undesired terms while keeping desired terms resolvable.

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“…We show the first inequality in (15) by presenting a converse proof for Theorem 1 in Section IV, which is based on similar arguments to those used in cache-aided PIR settings [20]. The second inequality in (15) is shown by a novel achievability scheme for Theorem 1 in Section V, which is based on distributed source coding [28].…”

Section: Main Results We Present Our Main Results In the Following Th...mentioning

confidence: 97%

Download Cost of Private Updating

Herren¹,

Arafa²,

Banawan³

2021

Preprint

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We consider the problem of privately updating a message out of K messages from N replicated and non-colluding databases. In this problem, a user has an outdated version of the message Ŵθ of length L bits that differ from the current version W θ in at most f bits. The user needs to retrieve W θ correctly using a private information retrieval (PIR) scheme with the least number of downloads without leaking any information about the message index θ to any individual database. To that end, we propose a novel achievable scheme based on syndrome decoding. Specifically, the user downloads the syndrome corresponding to W θ , according to a linear block code with carefully designed parameters, using the optimal PIR scheme for messages with a length constraint. We derive lower and upper bounds for the optimal download cost that match if the term log 2 f i=0 L i is an integer. Our results imply that there is a significant reduction in the download cost if f < L 2 compared with downloading W θ directly using classical PIR approaches without taking the correlation between W θ and Ŵθ into consideration.

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The Capacity of Multi-round Private Information Retrieval from Byzantine Databases

Cited by 13 publications

References 24 publications

Double Blind T-Private Information Retrieval

Double Blind T-Private Information Retrieval

Cross Subspace Alignment and the Asymptotic Capacity of $X$ -Secure $T$ -Private Information Retrieval

Download Cost of Private Updating

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