One-Shot PIR: Refinement and Lifting

D’Oliveira, Rafael G. L.; Rouayheb, Salim El

doi:10.1109/tit.2019.2954336

Cited by 29 publications

(12 citation statements)

References 23 publications

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“…If all φ b (x k ) are independent for all b, k, and furthermore H(φ b (x k )) = H(ρ (s) n (y n )) for all b, k, n, s, then the two expressions in (6) and (7) for the rate coincide. This is indeed the case given reasonable independence conditions on the data vectors and the functions to be evaluated, but for the sake of compactness and readability we will ignore these subtleties and use (6) as our definition of rate.…”

Section: E Private Computation Of Coded Datamentioning

confidence: 99%

Private Polynomial Computation From Lagrange Encoding

Raviv

Karpuk

2020

IEEE Trans.Inform.Forensic Secur.

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Private computation is a generalization of private information retrieval, in which a user is able to compute a function on a distributed dataset without revealing the identity of that function to the servers. In this paper it is shown that Lagrange encoding, a powerful technique for encoding Reed-Solomon codes, enables private computation in many cases of interest. In particular, we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data, while being robust to Byzantine and straggling servers, and to servers colluding to attempt to deduce the identities of the functions to be evaluated. Moreover, incorporating ideas from the well-known Shamir secret sharing scheme allows the data itself to be concealed from the servers as well. Our results extend private computation to high degree polynomials and to data-privacy, and reveal a tight connection between private computation and coded computation.

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Section: E Private Computation Of Coded Datamentioning

confidence: 99%

Private Polynomial Computation From Lagrange Encoding

Raviv

Karpuk

2020

IEEE Trans.Inform.Forensic Secur.

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“…Section IX-A considers the case of two servers and compares the achievable 4tuples R, U, ∆, ρ (•) for the (M, 2) WPIR schemes proposed in Sections IV-A, IV-C, V-A, and V-B. Section IX-B presents optimized values for the download rate for the time-sharing Scheme 1 by numerically solving the convex optimization problem in (18) for both the MI and MaxL privacy metrics and comparisons with the converse bounds from Theorems 7 and 9.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Thus, the optimization problem (18) under MI leakage is convex. However, it is difficult to have closed-form optimal solutions for (M, n) = (2, 2), and hence instead we present numerical results of the optimized time-sharing (M, 2) Scheme 1 for several values of the number of files M in Section IX.…”

Section: A Optimizing the MI Leakagementioning

confidence: 99%

“…In this subsection, we give the maximum download rate under a leakage constraint for the time-sharing Scheme 1 described in Section VI with both the MI and MaxL privacy metrics. Since for both metrics optimizing the download rate is a convex problem (see (18)), the optimal solutions can be obtained by using the CVXPY Python-embedded modeling language for convex optimization problems [51], [52]. The optimal corresponding rate obtained from ( 18) is denoted by R(•)…”

Section: B Optimized Rates For the Time-sharing Schemementioning

confidence: 99%

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Multi-Server Weakly-Private Information Retrieval

Lin

Kumar

Rosnes

et al. 2020

Preprint

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Private information retrieval (PIR) protocols ensure that a user can download a file from a database without revealing any information on the identity of the requested file to the servers storing the database. While existing protocols strictly impose that no information is leaked on the file's identity, this work initiates the study of the tradeoffs that can be achieved by relaxing the perfect privacy requirement. We refer to such protocols as weaklyprivate information retrieval (WPIR) protocols. In particular, for the case of multiple noncolluding replicated servers, we study how the download rate, the upload cost, and the access complexity can be improved when relaxing the full privacy constraint. To quantify the information leakage on the requested file's identity we consider mutual information (MI), worst-case information leakage, and maximal leakage (MaxL). We present two WPIR schemes based on two recent PIR protocols and show that the download rate of the former can be optimized by solving a convex optimization problem. Additionally, a family of schemes based on partitioning is presented. Moreover, we provide an informationtheoretic converse bound for the maximum possible download rate for the MI and MaxL privacy metrics under a practical restriction on the alphabet size of queries and answers. For two servers and two files, the bound is tight under the MaxL metric, which settles the WPIR capacity in this particular case. Finally, we compare the performance of the proposed schemes and their gap to the converse bound.

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“…Following [2], the capacity (or its reciprocal, the normalized download cost) of many variations of the problem have been investigated, see, e.g., [3]- [17].…”

Section: Introductionmentioning

confidence: 99%

Download Cost of Private Updating

Herren¹,

Arafa²,

Banawan³

2021

Preprint

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We consider the problem of privately updating a message out of K messages from N replicated and non-colluding databases. In this problem, a user has an outdated version of the message Ŵθ of length L bits that differ from the current version W θ in at most f bits. The user needs to retrieve W θ correctly using a private information retrieval (PIR) scheme with the least number of downloads without leaking any information about the message index θ to any individual database. To that end, we propose a novel achievable scheme based on syndrome decoding. Specifically, the user downloads the syndrome corresponding to W θ , according to a linear block code with carefully designed parameters, using the optimal PIR scheme for messages with a length constraint. We derive lower and upper bounds for the optimal download cost that match if the term log 2 f i=0 L i is an integer. Our results imply that there is a significant reduction in the download cost if f < L 2 compared with downloading W θ directly using classical PIR approaches without taking the correlation between W θ and Ŵθ into consideration.

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One-Shot PIR: Refinement and Lifting

Cited by 29 publications

References 23 publications

Private Polynomial Computation From Lagrange Encoding

Private Polynomial Computation From Lagrange Encoding

Multi-Server Weakly-Private Information Retrieval

Download Cost of Private Updating

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