Private information retrieval for coded storage

Chan, Terence; Ho, Siu-Wai; Yamamoto, Hirosuke

doi:10.1109/isit.2015.7282975

Cited by 178 publications

(203 citation statements)

References 17 publications

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“…This approach was first considered in [27], and several papers have developed this direction further, e.g. [2], [9], [10]. Our discussion on PIR will follow the breakthrough The authors are with the Department of Computer Science, Technion -Israel Institute of Technology, Haifa 3200003, Israel, (e-mail: {ywzhang,etzion,yaakobi}@cs.technion.ac.il).…”

Section: Introduction a General Backgroundmentioning

confidence: 99%

Bounds on the Length of Functional PIR and Batch Codes

Zhang

Etzion

Yaakobi

2020

IEEE Trans. Inform. Theory

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A functional k-PIR code of dimension s consists of n servers storing linear combinations of s linearly independent information symbols. Any linear combination of the s information symbols can be recovered by k disjoint subsets of servers. The goal is to find the smallest number of servers for given k and s. We provide lower bounds on the number of servers and constructions which yield upper bounds on this number. For k ≤ 4, exact bounds on the number of servers are proved. Furthermore, we provide some asymptotic bounds. The problem coincides with the well known private information retrieval problem based on a coded database to reduce the storage overhead, when each linear combination contains exactly one information symbol.If any multiset of size k of linear combinations from the linearly independent information symbols can be recovered by k disjoint subset of servers, then the servers form a functional k-batch code. A functional k-batch code is a functional k-PIR code, where all the k linear combinations in the multiset are equal. We provide some bounds on the number of servers for functional k-batch codes. In particular we present a random construction and a construction based on simplex codes, WOM codes, and RIO codes.

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Section: Introduction a General Backgroundmentioning

confidence: 99%

Bounds on the Length of Functional PIR and Batch Codes

Zhang

Etzion

Yaakobi

2020

IEEE Trans. Inform. Theory

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“…Recently, there has been a renewed interest to study the PIR problem from an information-theoretic formulation [5], [7], [8]. Under this setting, the file size is assumed to be arbitrarily large, and hence the upload cost can be ignored compared to the download cost.…”

Section: Introductionmentioning

confidence: 99%

Weakly-Private Information Retrieval

Lin

Kumar

Rosnes

et al. 2019

2019 IEEE International Symposium on Information Theory (ISIT)

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Private information retrieval (PIR) protocols make it possible to retrieve a file from a database without disclosing any information about the identity of the file being retrieved. These protocols have been rigorously explored from an informationtheoretic perspective in recent years. While existing protocols strictly impose that no information is leaked on the file's identity, this work initiates the study of the tradeoffs that can be achieved by relaxing the requirement of perfect privacy. In case the user is willing to leak some information on the identity of the retrieved file, we study how the PIR rate, as well as the upload cost and access complexity, can be improved. For the particular case of replicated servers, we propose two weakly-private information retrieval schemes based on two recent PIR protocols and a family of schemes based on partitioning. Lastly, we compare the performance of the proposed schemes.

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“…The user compresses the queries to these databases by adding the individual symbols in round 1 into single equation. 4 4. Repeat step 2, 3 over new blocks of 4 symbols for K 2 repetitions.…”

Section: Compressing Queriesmentioning

confidence: 99%

“…In the classical setting, a user is interested in retrieving a single message (file) out of K messages from N replicated and non-colluding databases, in such a way that no database can know the identity of the user's desired file. The PIR problem has become a vibrant research topic within information theory starting with trailblazing papers [2][3][4][5][6][7][8]. In [9], Sun and Jafar introduce the PIR capacity, which is the supremum of the ratio of the number of bits of desired information (L) that can be retrieved privately to the total downloaded information.…”

Section: Introductionmentioning

confidence: 99%

Private Information Retrieval from Non-Replicated Databases

Banawan

Ulukuş

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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We consider the problem of private information retrieval (PIR) of a single message out of K messages from N non-colluding and non-replicated databases. Different from the majority of the existing literature, which considers the case of replicated databases where all databases store the same content in the form of all K messages, here, we consider the case of non-replicated databases under a special non-replication structure where each database stores M out of K messages and each message is stored across R different databases. This generates an R-regular graph structure for the storage system where the vertices of the graph are the messages and the edges are the databases. We derive a general upper bound for M = 2 that depends on the graph structure. We then specialize the problem to storage systems described by two special types of graph structures: cyclic graphs and fully-connected graphs. We prove that the PIR capacity for the case of cyclic graphs is 2 K+1 , and the PIR capacity for the case of fully-connected graphs is min{ 2 K , 1 2 }. To that end, we propose novel achievable schemes for both graph structures that are capacity-achieving. The central insight in both schemes is to introduce dependency in the queries submitted to databases that do not contain the desired message, such that the requests can be compressed. In both cases, the results show severe degradation in PIR capacity due to non-replication.

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Private information retrieval for coded storage

Cited by 178 publications

References 17 publications

Bounds on the Length of Functional PIR and Batch Codes

Bounds on the Length of Functional PIR and Batch Codes

Weakly-Private Information Retrieval

Private Information Retrieval from Non-Replicated Databases

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