2-Server PIR with Sub-Polynomial Communication

Dvir, Zeev; Gopi, Sivakanth

doi:10.1145/2746539.2746546

Cited by 52 publications

(50 citation statements)

References 26 publications

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“…Clearly, the choice α φ A vf ,eφ /γ f satisfies (9), and consequently, h Av g ,e φ γgαφ satisfies (8). We are only left to show that this value for h is neither 0 nor 1.…”

Section: Lemma 14mentioning

confidence: 97%

Private Information Retrieval in Graph-Based Replication Systems

Raviv

Tamo

Yaakobi

2020

IEEE Trans. Inform. Theory

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In a Private Information Retrieval (PIR) protocol, a user can download a file from a database without revealing the identity of the file to each individual server. A PIR protocol is called t-private if the identity of the file remains concealed even if t of the servers collude. Graph based replication is a simple technique, which is prevalent in both theory and practice, for achieving erasure robustness in storage systems. In this technique each file is replicated on two or more storage servers, giving rise to a (hyper-)graph structure. In this paper we study private information retrieval protocols in graph based replication systems. The main interest of this work is maximizing the parameter t, and in particular, understanding the structure of the colluding sets which emerge in a given graph. Our main contribution is a 2-replication scheme which guarantees perfect privacy from acyclic sets in the graph, and guarantees partialprivacy in the presence of cycles. Furthermore, by providing an upper bound, it is shown that the PIR rate of this scheme is at most a factor of two from its optimal value for an important family of graphs. Lastly, we extend our results to larger replication factors and to graph-based coding, which is a similar technique with smaller storage overhead and larger PIR rate.Parts of this work were presented at the International Symposium on Information Theory (ISIT), Vail, CO, USA, 2018. 1 In some settings, only computational privacy is required, but this paper focus exclusively on perfect privacy.   ,which naturally corresponds to the setsAs another example, in which N − K ≥ K, we may consider the following.Example 18. Assume that N − K = 6 and K = 4, which implies that r = 2 and b = 3. Consider the following matrix 1 1 1 1 2 2 2 2 3 3 3 3 which naturally corresponds to the sets J (1,1) = {1, 2, 3, 4} J (2,1) = ∅ J (1,2) = {5, 6} J (2,2) = {1, 2} J (1,3) = ∅ J (2,3) = {3, 4, 5, 6}.

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“…Clearly, the choice α φ A vf ,eφ /γ f satisfies (9), and consequently, h Av g ,e φ γgαφ satisfies (8). We are only left to show that this value for h is neither 0 nor 1.…”

Section: Lemma 14mentioning

confidence: 97%

Private Information Retrieval in Graph-Based Replication Systems

Raviv

Tamo

Yaakobi

2020

IEEE Trans. Inform. Theory

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“…Suppose that C = RM (0, 4) = Rep(16) 2 , so that data is stored via a replication system over n = 16 servers. Set D = RM (1,4), which is a [16,5,8]…”

Section: B Achievable Pir Rate With Reed-muller Codesmentioning

confidence: 99%

$t$-private information retrieval schemes using transitive codes

Freij-Hollanti

Gnilke

Hollanti

et al. 2019

IEEE Trans. Inform. Theory

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This paper presents private information retrieval (PIR) schemes for coded storage with colluding servers, which are not restricted to maximum distance separable (MDS) codes. PIR schemes for general linear codes are constructed and the resulting PIR rate is calculated explicitly. It is shown that codes with transitive automorphism groups yield the highest possible rates obtainable with the proposed scheme.This rate coincides with the known asymptotic PIR capacity for MDS-coded storage systems without collusion. While many PIR schemes in the literature require field sizes that grow with the number of servers and files in the system, we focus especially on the case of a binary base field, for which Reed-Muller codes serve as an important and explicit class of examples.

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“…As discussed above, the word size can not be pushed beyond 2 Θ( √ log n) due to known constructions [DG15].…”

Section: Open Problems We Compile a List Of Exciting Open Problemsmentioning

confidence: 99%

Optimal Hashing-based Time-Space Trade-offs for Approximate Near Neighbors

Andoni

Laarhoven

Razenshteyn³

et al. 2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

150

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We show tight upper and lower bounds for time-space trade-offs for the c-approximate Near Neighbor Search problem. For the d-dimensional Euclidean space and npoint datasets, we develop a data structure with space n 1+ρu+o(1) + O(dn) and query time n ρq+o(1) + dn o(1) for every ρ u , ρ q ≥ 0 with:In particular, for the approximation c = 2 we get:• Space n 1.77... and query time n o(1) , significantly improving upon known data structures that support very fast queries [IM98, KOR00];• Space n 1.14... and query time n 0.14... , matching the optimal data-dependent Locality-Sensitive Hashing (LSH) from [AR15];• Space n 1+o(1) and query time n 0.43... , making significant progress in the regime of near-linear space, which is arguably of the most interest for prac-This is the first data structure that achieves sublinear query time and near-linear space for every approximation factor c > 1, improving upon [Kap15]. The data structure is a culmination of a long line of work on the problem for all space regimes; it builds on Spherical Locality-Sensitive Filtering [BDGL16] and datadependent hashing [AINR14, AR15]. Our matching lower bounds are of two types: conditional and unconditional. First, we prove tightness of the whole trade-off (0.1) in a restricted model of computation, which captures all known hashing-based approaches. We then show unconditional cell-probe lower * This paper merges two arXiv preprints: [Laa15c] (appeared online on November 24, 2015) and [ALRW16] (appeared online on May 9, 2016), and subsumes both of these articles. The full version containing all the proofs is available at https://arxiv.org/abs/1608.03580 bounds for one and two probes that match (0.1) for ρ q = 0, improving upon the best known lower bounds from [PTW10]. In particular, this is the first space lower bound (for any static data structure) for two probes which is not polynomially smaller than the one-probe bound. To show the result for two probes, we establish and exploit a connection to locally-decodable codes.

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2-Server PIR with Sub-Polynomial Communication

Cited by 52 publications

References 26 publications

Private Information Retrieval in Graph-Based Replication Systems

Private Information Retrieval in Graph-Based Replication Systems

$t$-private information retrieval schemes using transitive codes

Optimal Hashing-based Time-Space Trade-offs for Approximate Near Neighbors

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