The Capacity of Private Information Retrieval from Decentralized Uncoded Caching Databases

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

doi:10.48550/arxiv.1811.11160

Cited by 6 publications

(7 citation statements)

References 47 publications

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“…which follows similar reasoning as (25). From (26), we see that each answer Āk is protected by a randomness Sk , and as long as the eavesdropper sees no more than L F many answers, the corresponding L F number of Ss are linearly independent, due to the MDS property of the generating matrix G ( L, L F ) . Hence, the inner product of the corresponding query vector and message vector is fully protected against the passive eavesdropper who observes answers from servers in E m .…”

Section: The Number Of Query Vectors Each Colluding Setmentioning

confidence: 53%

The Capacity of Symmetric Private Information Retrieval under Arbitrary Collusion and Eavesdropping Patterns

Cheng¹,

Liu²,

Kang³

2020

Preprint

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We study the symmetric private information retrieval (SPIR) problem under arbitrary collusion and eavesdropping patterns for replicated databases. We find its capacity, which is the same as the capacity of the original SPIR problem with the number of databases N replaced by a number F * . The number F * is the optimal solution to a linear programming problem that is a function of the joint pattern, which is the union of the collusion and eavesdropping pattern. This is the first result that shows how two arbitrary patterns collectively affect the capacity of the PIR problem. We draw the conclusion that for SPIR problems, the collusion and eavesdropping constraints are interchangeable in terms of capacity.As special cases of our result, the capacity of the SPIR problem under arbitrary collusion patterns and the capacity of the PIR problem under arbitrary eavesdropping patterns are also found. I. INTRODUCTIONIn a computer network based on a client-server model, the behavior of information retrieval is often related to privacy leaks. A malicious server that monitors user queries will retrieve the server's history and infer the user's behavior in conjunction with other servers. Simultaneously, the privacy of the database often needs to be protected as well, i.e., the user cannot get more information than the desired message. For data queries, especially in the case of information

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Section: The Number Of Query Vectors Each Colluding Setmentioning

confidence: 53%

The Capacity of Symmetric Private Information Retrieval under Arbitrary Collusion and Eavesdropping Patterns

Cheng¹,

Liu²,

Kang³

2020

Preprint

View full text Add to dashboard Cite

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“…Furthermore, the proof techniques therein may be useful to derive the minimum L for a SC-PIR problem. Second, another work [6] has considered random placement among databases where a database stores a bit of a given message with probability µ. Interestingly, this placement method was also used in [11] for the coded caching problem. It will be meaningful to examine alternative random placement strategies for the SC-PIR problem where messages are split into a finite number of sub-messages.…”

Section: Discussion and Future Workmentioning

confidence: 99%

“…Hence, the proposed PIR scheme of [2] can be impractical for a large number of databases. This achievable scheme was generalized to the decentralized storage placement in [6]. Furthermore, Tian et al [7] use Shannon theoretic approach to analyze the SC-PIR problem for the canonical case of K = 2 and N = 2 and proposed the optimal linear scheme.…”

Section: Introductionmentioning

confidence: 99%

A New Design of Private Information Retrieval for Storage Constrained Databases

Woolsey

Chen

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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Private information retrieval (PIR) allows a user to download one of K messages from N databases without revealing to any database which of the K messages is being downloaded. In general, the databases can be storage constrained where each database can only store up to µKL bits where 1 N ≤ µ ≤ 1 and L is the size of each message in bits. Let t = µN , a recent work showed that the capacity of Storage Constrained PIR (SC-PIR)−1 , which is achieved by a storage placement scheme inspired by the content placement scheme in the literature of coded caching and the original PIR scheme. Not surprisingly, this achievable scheme requires that each message is L = N t t K bits in length, which can be impractical. In this paper, without trying to make the connection between SC-PIR and coded caching problems, based on a general connection between the Full Storage PIR (FS-PIR) problem (µ = 1) and SC-PIR problem, we propose a new SC-PIR design idea using novel storage placement schemes. The proposed schemes significantly reduce the message size requirement while still meeting the capacity of SC-PIR. In particular, the proposed SC-PIR schemes require the size of each file to be only L = N t K−1 compared to the state-of-the-art L = N t t K . Hence, we conclude that PIR may not meet coded caching when the size of L is constrained.

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“…, N . This problem is then extended to the decentralized setting in [35], where the contents are stored independently across databases according to a probability distribution, and to the heterogeneous setting in [40] where the databases have heterogeneous storage sizes. In all these works, with the exception of [12], the fundamental limits are derived for uncoded storage strategies.…”

Section: Introductionmentioning

confidence: 99%

Improved Storage for Efficient Private Information Retrieval

Banawan

Arasli

Ulukuş

2019

2019 IEEE Information Theory Workshop (ITW)

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We consider the problem of private information retrieval from N storage-constrained databases. In this problem, a user wishes to retrieve a single message out of M messages (of size L) without revealing any information about the identity of the message to individual databases. Each database stores µM L symbols, i.e., a µ fraction of the entire library, where 1 N ≤ µ ≤ 1. Our goal is to characterize the optimal tradeoff curve for the storage cost (captured by µ) and the normalized download cost (D/L). We show that the download cost can be reduced by employing a hybrid storage scheme that combines MDS coding ideas with uncoded partial replication ideas. When there is no coding, our scheme reduces to Attia-Kumar-Tandon storage scheme, which was initially introduced by Maddah-Ali-Niesen in the context of the caching problem, and when there is no uncoded partial replication, our scheme reduces to Banawan-Ulukus storage scheme; in general, our scheme outperforms both.

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The Capacity of Private Information Retrieval from Decentralized Uncoded Caching Databases

Cited by 6 publications

References 47 publications

The Capacity of Symmetric Private Information Retrieval under Arbitrary Collusion and Eavesdropping Patterns

The Capacity of Symmetric Private Information Retrieval under Arbitrary Collusion and Eavesdropping Patterns

A New Design of Private Information Retrieval for Storage Constrained Databases

Improved Storage for Efficient Private Information Retrieval

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