The Capacity of Uncoded Storage Constrained PIR

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

doi:10.1109/isit.2018.8437729

Cited by 10 publications

(14 citation statements)

References 11 publications

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“…All permutations are generated by the user and are not known to the servers. First, the single symbol a 1 12 is downloaded from Serv 1 . In fact, we download the symbol a 1 12 or a 2 12 depending on the random permutation.…”

Section: The Pir Scheme Withmentioning

confidence: 99%

“…First, the single symbol a 1 12 is downloaded from Serv 1 . In fact, we download the symbol a 1 12 or a 2 12 depending on the random permutation. Because of the requirement of message symmetry, b 1 12 is also requested and downloaded.…”

Section: The Pir Scheme Withmentioning

confidence: 99%

“…Our contribution. For arbitrary N , M and 1 ≤ t < N , we prove that t M −1 is a factor of sub-packetization L for any capacity-achieving PIR scheme from storage constrained servers, and design a PIR scheme with sub-packetization L = N t × t M −1 which achieves minimum possible download cost D(t) in (1). Comparing with the scheme in [16,17], our scheme has a reduced sub-packetization parameter L by a factor t. In particular, the improvement amounts to reduction by t times to the number of requests to servers.…”

Section: Introductionmentioning

confidence: 95%

“…The original concept of PIR [1] was proposed by Chor et al in 1995. In practice, many applications are related to private information retrieval problems, like protecting the identity of stock market records reviewed by an investor or protecting the nature of restricted content browsed by activists on the internet in oppressive regimes.…”

Section: Introductionmentioning

confidence: 99%

“…. The information-theoretical description of the PIR problem can be found in [16] where the following lower bound for download cost (DC) was obtained (1) D ≥ D(t) = 1 + 1/t + 1/t…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Capacity-achieving private information retrieval scheme with a smaller sub-packetization

Zhang¹,

Zhou²,

Parampalli³

et al. 2021

Advances in Mathematics of Communications

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Private information retrieval (PIR) allows a user to retrieve one out of M messages from N servers without revealing the identity of the desired message. Every message consists of L symbols (packets) from an additive group and the length L is called the sub-packetization. A PIR scheme with download cost (DC) D/L is implemented by querying D sums of the symbols to servers. We assume that each uncoded server can store up to tLM/N symbols, t ∈ {1, 2, • • • , N }. The minimum DC of storage constrained PIR was determined by Attia et al. in 2018 to be DC min = 1 + 1/t + 1/t 2 + • • • + 1/t M −1. The capacity of storage constrained PIR (equivalently, the reciprocal of minimum download cost) is the maximum number of bits of desired symbols that can be privately retrieved per bit of downloaded symbols. Tandon et al. designed a capacity-achieving PIR scheme with sub-packetization L = N t t M of each message. In this paper, we design a PIR scheme with t times smaller subpacketization L /t and with the minimum DC for any parameters N, M, t. We also prove that t M −1 is a factor of sub-packetization L for any capacityachieving PIR scheme from storage constrained servers.

show abstract

Section: The Pir Scheme Withmentioning

confidence: 99%

Section: The Pir Scheme Withmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

“…. The information-theoretical description of the PIR problem can be found in [16] where the following lower bound for download cost (DC) was obtained (1) D ≥ D(t) = 1 + 1/t + 1/t…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Capacity-achieving private information retrieval scheme with a smaller sub-packetization

Zhang¹,

Zhou²,

Parampalli³

et al. 2021

Advances in Mathematics of Communications

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show abstract

Private Sequential Function Computation

Tahmasebi

Maddah-Ali

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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In this paper, we introduce the problem of private sequential function computation, where a user wishes to compute a composition of a sequence of K linear functions, in a specific order, for an arbitrary input. The user does not run these computations locally, rather it exploits the existence of N non-colluding servers, each can compute any of the K functions on any given input. However, the user does not want to reveal any information about the desired order of computations to the servers. For this problem, we study the capacity C, defined as the supremum of the number of desired computations, normalized by the number of computations done at the servers, subject to the privacy constraint. In particular, we prove thatFor the achievability, we show that the user can retrieve the desired order of computations, by choosing a proper order of inquiries among different servers, while keeping the order of computations for each server fixed, irrespective of the desired order of computations. In the end, we develop an information-theoretic converse which results an upper bound on the capacity.

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Private Information Retrieval From a Cellular Network With Caching at the Edge

Kumar

Amat

Rosnes

et al. 2019

IEEE Trans. Commun.

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We consider the problem of downloading content from a cellular network where content is cached at the wireless edge while achieving privacy. In particular, we consider private information retrieval (PIR) of content from a library of files, i.e., the user wishes to download a file and does not want the network to learn any information about which file she is interested in. To reduce the backhaul usage, content is cached at the wireless edge in a number of small-cell base stations (SBSs) using maximum distance separable codes. We propose a PIR scheme for this scenario that achieves privacy against a number of spy SBSs that (possibly) collaborate. The proposed PIR scheme is an extension of a recently introduced scheme by Kumar et al. to the case of multiple code rates, suitable for the scenario where files have different popularities. We then derive the backhaul rate and optimize the content placement to minimize it. We prove that uniform content placement is optimal, i.e., all files that are cached should be stored using the same code rate. This is in contrast to the case where no PIR is required. Furthermore, we show numerically that popular content placement is optimal for some scenarios.

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The Capacity of Uncoded Storage Constrained PIR

Cited by 10 publications

References 11 publications

Capacity-achieving private information retrieval scheme with a smaller sub-packetization

Capacity-achieving private information retrieval scheme with a smaller sub-packetization

Private Sequential Function Computation

Private Information Retrieval From a Cellular Network With Caching at the Edge

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