Codes for distributed PIR with low storage overhead

Fazeli, Arman; Vardy, Alexander; Yaakobi, Eitan

doi:10.1109/isit.2015.7282977

Cited by 133 publications

(119 citation statements)

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“…If the k requests are the same (linear combination) then the scheme will be called a functional k-PIR code and furthermore if these k requests contain the same information symbol, then the scheme will be called a k-PIR code. This definition for k-PIR coincides with the definition for k-PIR given in [15], [16] for a single user. Let F B(s, k) (B(s, k), F P (s, k), P (s, k), respectively) be the minimum number of servers required for s items and k requests for functional k-batch (kbatch, functional k-PIR, k-PIR, respectively).…”

Section: B General Description Of the Problemsupporting

confidence: 65%

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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: B General Description Of the Problemsupporting

confidence: 65%

“…Our goal in this paper is to obtain lower and upper bounds on F B(s, k) and F P (s, k), since relatively good bounds on B(s, k) and P (s, k) are known from the literature. Some of these bounds on B(s, k) and P (s, k) were derived in [1], [5], [15], [20], [23], [25], [30], [34] and are summarized as follows.…”

Section: Basic Resultsmentioning

confidence: 99%

Bounds on the Length of Functional PIR and Batch Codes

Zhang

Etzion

Yaakobi

2020

IEEE Trans. Inform. Theory

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“…We then check the following. 1) Information leakage: in view of the performance of TSC code in (19) and (22), the overall normalized total leakage is…”

Section: B Achievability Of Pareto Optimal Pointsmentioning

confidence: 99%

On the Information Leakage in Private Information Retrieval Systems

Guo

Zhou

Tian

2020

IEEE Trans.Inform.Forensic Secur.

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We consider information leakage to the user in private information retrieval (PIR) systems. Information leakage can be measured in terms of individual message leakage or total leakage. Individual message leakage, or simply individual leakage, is defined as the amount of information that the user can obtain on any individual message that is not being requested, and the total leakage is defined as the amount of information that the user can obtain about all the other messages except the one being requested. In this work, we characterize the tradeoff between the minimum download cost and the individual leakage, and that for the total leakage, respectively. New codes are proposed to achieve these optimal tradeoffs, which are also shown to be optimal in terms of the message size. We further characterize the optimal tradeoff between the minimum amount of common randomness and the total leakage. Moreover, we show that under individual leakage, common randomness is in fact unnecessary when there are more than two messages.

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“…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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Codes for distributed PIR with low storage overhead

Cited by 133 publications

References 13 publications

Bounds on the Length of Functional PIR and Batch Codes

Bounds on the Length of Functional PIR and Batch Codes

On the Information Leakage in Private Information Retrieval Systems

Private Information Retrieval from Non-Replicated Databases

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