On the Information Leakage in Private Information Retrieval Systems

Guo, Tao; Zhou, Ruida; Tian, Chao

doi:10.48550/arxiv.1909.11605

Cited by 8 publications

(12 citation statements)

References 37 publications

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“…In another recent work, Guo et al [58] considered the problem of SPIR with perfect user privacy and relaxed DB privacy. DB privacy was relaxed by allowing a bounded mutual information (no more than δ) between the undesired messages, the queries, and the answers received by the user.…”

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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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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“…Remark 1 The condition in (12) is a statement about the sum weighted (by 1 N i−1 ) deviation of message size from its expected value. Note that the expected value of the message size E[L] is a function of the message sizes L i and the prior distribution p i for i = 1, .…”

Section: Main Results and Discussionmentioning

confidence: 99%

Semantic Private Information Retrieval

Sajani¹,

Banawan²,

Ulukuş³

2020

Preprint

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We investigate the problem of semantic private information retrieval (semantic PIR). In semantic PIR, a user retrieves a message out of K independent messages stored in N replicated and non-colluding databases without revealing the identity of the desired message to any individual database. The messages come with different semantics, i.e., the messages are allowed to have non-uniform a priori probabilities denoted by (p i > 0, i ∈ [K]), which are a proxy for their respective popularity of retrieval, and arbitrary message sizes). This is a generalization of the classical private information retrieval (PIR) problem, where messages are assumed to have equal a priori probabilities and equal message sizes. We derive the semantic PIR capacity for general K, N . The results show that the semantic PIR capacity depends on the number of databases N , the number of messages K, the a priori probability distribution of messages p i , and the message sizes L i . We present two achievable semantic PIR schemes: The first one is a deterministic scheme which is based on message asymmetry. This scheme employs non-uniform subpacketization. The second scheme is probabilistic and is based on choosing one query set out of multiple options at random to retrieve the required message without the need for exponential subpacketization. We derive necessary and sufficient conditions for the semantic PIR capacity to exceed the classical PIR capacity with equal priors and sizes. Our results show that the semantic PIR capacity can be larger than the classical PIR capacity when longer messages have higher popularities. However, when messages are equal-length, the non-uniform priors cannot be exploited to improve the retrieval rate over the classical PIR capacity.

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“…The first is the corner point corresponding to the scheme [32, Table III] with τ 2 = 3 7 , i.e., with d 1 = 8, and d 2 = 6. 6 This gives pAoI(R min ) 2µ…”

Section: A Peak-age Minimization Under Perfect Privacymentioning

confidence: 99%

Timely Private Information Retrieval

Banawan¹,

Arafa²,

Ulukuş³

2021

Preprint

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We introduce the problem of timely private information retrieval (PIR) from N non-colluding and replicated servers. In this problem, a user desires to retrieve a message out of M messages from the servers, whose contents are continuously updating. The retrieval process should be executed in a timely manner such that no information is leaked about the identity of the message. To assess the timeliness, we use the age of information (AoI) metric. Interestingly, the timely PIR problem reduces to an AoI minimization subject to PIR constraints under asymmetric traffic. We explicitly characterize the optimal tradeoff between the PIR rate and the AoI metric (peak AoI or average AoI) for the case of N = 2, M = 3. Further, we provide some structural insights on the general problem with arbitrary N , M .

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On the Information Leakage in Private Information Retrieval Systems

Cited by 8 publications

References 37 publications

On the Capacity of Leaky Private Information Retrieval

On the Capacity of Leaky Private Information Retrieval

Semantic Private Information Retrieval

Timely Private Information Retrieval

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