The Capacity of Private Information Retrieval from Uncoded Storage Constrained Databases

Attia, Mohamed Adel; Kumar, Deepak; Tandon, Ravi

doi:10.48550/arxiv.1805.04104

Cited by 15 publications

(85 citation statements)

References 29 publications

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Section: Introductionmentioning

confidence: 99%

“…Reference [36] studies PIR from homogeneous storage-limited databases. In [36], each database has the same limited storage space of µKL bits with 0 ≤ µ ≤ 1, where L is the message size (note, perfect replication would have required µ = 1). The goal of [36] is to find the optimal centralized uncoded caching scheme (content placement) that minimizes the PIR download cost.…”

Section: Introductionmentioning

confidence: 99%

“…In [36], each database has the same limited storage space of µKL bits with 0 ≤ µ ≤ 1, where L is the message size (note, perfect replication would have required µ = 1). The goal of [36] is to find the optimal centralized uncoded caching scheme (content placement) that minimizes the PIR download cost. [36] shows that symmetric batch caching scheme of [54] for content placement together with Sun-Jafar scheme in [7] for information retrieval result in the lowest normalized download cost.…”

Section: Introductionmentioning

confidence: 99%

“…The goal of [36] is to find the optimal centralized uncoded caching scheme (content placement) that minimizes the PIR download cost. [36] shows that symmetric batch caching scheme of [54] for content placement together with Sun-Jafar scheme in [7] for information retrieval result in the lowest normalized download cost. [36] characterizes the optimal storage-download cost trade-off as the lower convex hull of N pairs ( t N , 1…”

Section: Introductionmentioning

confidence: 99%

“…We aim to characterize the optimal normalized PIR download cost of this problem, and the corresponding optimal placement and optimal retrieval schemes. We focus on uncoded placement as in [36] and [55].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The Capacity of Private Information Retrieval from Heterogeneous Uncoded Caching Databases

Banawan¹,

Arasli²,

Wei³

et al. 2019

Preprint

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We consider private information retrieval (PIR) of a single file out of K files fromThe aim of this work is to jointly design the content placement phase and the information retrieval phase in order to minimize the download cost in the PIR phase. We characterize the optimal PIR download cost as a linear program. By analyzing the structure of the optimal solution of this linear program, we show that, surprisingly, the optimal download cost in our heterogeneous case matches its homogeneous counterpart where all databases have the same average storage constraint µ = 1 N N n=1 m n . Thus, we show that there is no loss in the PIR capacity due to heterogeneity of storage spaces of the databases. We provide the optimum content placement explicitly for N = 3.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Capacity of Private Information Retrieval from Heterogeneous Uncoded Caching Databases

Banawan¹,

Arasli²,

Wei³

et al. 2019

Preprint

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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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On the Capacity of Leaky Private Information Retrieval

Samy

Tandon

Lazos

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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Information-theoretic formulations of the private information retrieval (PIR) problem have been investigated under a variety of scenarios. Symmetric private information retrieval (SPIR) is a variant where a user is able to privately retrieve one out of K messages from N noncolluding replicated databases without learning anything about the remaining K − 1 messages. However, the goal of perfect privacy can be too taxing for certain applications. In this paper, we investigate if the information-theoretic capacity of SPIR (equivalently, the inverse of the minimum download cost) can be increased by relaxing both user and DB privacy definitions. Such relaxation is relevant in applications where privacy can be traded for communication efficiency.We introduce and investigate the Asymmetric Leaky PIR (AL-PIR) model with different privacy leakage budgets in each direction. For user privacy leakage, we bound the probability ratios between all possible realizations of DB queries by a function of a non-negative constant . For DB privacy, we bound the mutual information between the undesired messages, the queries, and the answers, by a function of a non-negative constant δ. We propose a general AL-PIR scheme that achieves an upper bound on the optimal download cost for arbitrary and δ. We show that the optimal download cost of AL-PIR is upper-bounded as D * ( , δ) ≤ 1 + 1 N −1 − δe N K−1 −1 . Second, we obtain an information-theoretic lower bound on the download cost asThe gap analysis between the two bounds shows that our AL-PIR scheme is optimal when = 0, i.e., under perfect user privacy and it is optimal within a maximum multiplicative gap of N −e − N −1 for any > 0 and δ > 0.to retrieve information privately by executing a private information retrieval (PIR) protocol. In a PIR protocol, the identity of the message retrieved by the user remains secret from the database(s). This is typically achieved at the expense of an increased communication cost to ensure that the desired message remains hidden among others. In the pioneering work by Chor et al.[1], the authors considered one-bit long messages. The overhead was calculated as the sum of the queries sent by the user (upload cost) and the answers provided by the database (download cost). Under arbitrarily large messages, the download cost becomes the dominant factor of the PIR overhead. This allows the PIR rate to be defined as the ratio of the message size to the number of downloaded bits. The maximum of these rates is referred to as the PIR capacity and its reciprocal as the download cost.Since the introduction of the PIR problem in [1], an extensive body of works have investigated efficient PIR schemes that yield either computational [2][3][4][5] or information-theoretic privacy guarantees . The former achieves privacy assuming computational limitations at the DBs, where cryptographic assumptions are invoked to preserve privacy such that NP-hard computations are required to reveal the requested message identity. In information-theoretic PIR, the DBs are assumed to be com...

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The Capacity of Private Information Retrieval from Uncoded Storage Constrained Databases

Cited by 15 publications

References 29 publications

The Capacity of Private Information Retrieval from Heterogeneous Uncoded Caching Databases

The Capacity of Private Information Retrieval from Heterogeneous Uncoded Caching Databases

Private Information Retrieval from Non-Replicated Databases

On the Capacity of Leaky Private Information Retrieval

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