Private Information Retrieval from Heterogeneous Uncoded Caching Databases

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

doi:10.1109/isit.2019.8849652

Cited by 5 publications

(1 citation statement)

References 35 publications

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“…The problem of PIR was also studied when the user has a cache or side-information, which can be useful in increasing PIR capacity [28][29][30][31][32]. PIR from storage-constrained databases was studied in [33,43,44], where capacity was characterized under the assumption of uncoded storage across databases. Recently, Tian et al [34] proposed a new capacity-achieving scheme with an optimal message size of N − 1 and a minimum upload cost.…”

Section: Introductionmentioning

confidence: 99%

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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