Achieving Maximum Distance Separable Private Information Retrieval Capacity With Linear Codes

Kumar, Siddhartha; Lin, Hsuan-Yin; Rosnes, Eirik; Amat, Alexandre Graell i

doi:10.1109/tit.2019.2900313

Cited by 104 publications

(103 citation statements)

References 47 publications

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“…7) Privacy: It is worth mentioning that the queries generated by Algorithm 1 inherently satisfy the privacy condition of (2a), which is guaranteed by satisfying the index, message, and database symmetry principles as for all the PIR schemes in [11], [13], [16]. We also would like to emphasize that the achievable rates of our proposed PC schemes can be further improved by removing the redundant queries caused from the dependency among the virtual messages.…”

Section: Algorithm 1: Q-genmentioning

confidence: 96%

“…Now, we are ready for the converse proof. By [16,Lem. 2], since the code C is MDS-PIR capacity-achieving, there exist ν information sets I 1 , .…”

Section: (V)mentioning

confidence: 99%

“…Accordingly, one can easily see that the [4,2] code C given in Example 1 is an MDS-PIR capacity-achieving code. Note that the class of MDS-PIR capacity-achieving codes includes MDS codes, cyclic codes, Reed-Muller codes, and certain classes of distance-optimal local reconstruction codes [16].…”

Section: Mds-pir Capacity-achieving Codesmentioning

confidence: 99%

“…Generate query sets for the initial round Generate desired symbols for the following rounds τ > 1 16 for…”

Section: Algorithm 1: Q-genmentioning

confidence: 99%

“…One of the main results of this paper is the derivation of the PLC capacity for a coded DSS where data is encoded and stored using a linear code from the class of MDS-PIR capacity-achieving codes [16]. The problem of PLC translates, in the PPC setup, to restricting the candidate function set to polynomials of degree g = 1.…”

Section: Private Linear Computation From Coded Dsssmentioning

confidence: 99%

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Private Polynomial Computation for Noncolluding Coded Databases

Obead

Lin

Rosnes

et al. 2019

2019 IEEE International Symposium on Information Theory (ISIT)

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Private computation in a distributed storage system (DSS) is a generalization of the private information retrieval (PIR) problem. In such setting a user wishes to compute a function of f messages stored in noncolluding coded databases while revealing no information about the desired function to the databases. We consider the problem of private polynomial computation (PPC). In PPC, a user wishes to compute a multivariate polynomial of degree at most g over f variables (or messages) stored in multiple databases. First, we consider the private computation of polynomials of degree g = 1, i.e., private linear computation (PLC) for coded databases. In PLC, a user wishes to compute a linear combination over the f messages while keeping the coefficients of the desired linear combination hidden from the database. For a linearly encoded DSS, we present a capacity-achieving PLC scheme and show that the PLC capacity, which is the ratio of the desired amount of information and the total amount of downloaded information, matches the maximum distance separable coded capacity of PIR for a large class of linear storage codes. Then, we consider private computation of higher degree polynomials, i.e., g > 1. For this setup, we construct two novel PPC schemes. In the first scheme we consider Reed-Solomon coded databases with Lagrange encoding, which leverages ideas from recently proposed star-product PIR and Lagrange coded computation. The second scheme considers the special case of coded databases with systematic Lagrange encoding. Both schemes yield improved rates compared to the best known schemes from the literature for a small number of messages, while asymptotically, as f → ∞, the systematic scheme gives a significantly better computation rate compared to all known schemes up to some storage code rate that depends on the maximum degree of the candidate polynomials.

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Section: Algorithm 1: Q-genmentioning

confidence: 96%

“…Now, we are ready for the converse proof. By [16,Lem. 2], since the code C is MDS-PIR capacity-achieving, there exist ν information sets I 1 , .…”

Section: (V)mentioning

confidence: 99%

Section: Mds-pir Capacity-achieving Codesmentioning

confidence: 99%

“…Generate query sets for the initial round Generate desired symbols for the following rounds τ > 1 16 for…”

Section: Algorithm 1: Q-genmentioning

confidence: 99%

Section: Private Linear Computation From Coded Dsssmentioning

confidence: 99%

See 3 more Smart Citations

Private Polynomial Computation for Noncolluding Coded Databases

Obead

Lin

Rosnes

et al. 2019

2019 IEEE International Symposium on Information Theory (ISIT)

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Robust private information retrieval for low encoding/decoding complexity distributed storage

Dai

Deng

et al. 2022

IET Information Security

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Private information retrieval (PIR) means a user retrieves a file while revealing no information on which file is being retrieved. In classic PIR, the user needs to wait for the responses of all the storage nodes. However, in general, there may be some nodes that are unresponsive, in which case it is formulated as v-robust PIR in the network coding (NC) structured distributed storage system (DSS), where v denotes the number of unresponsive nodes. We consider PIR with unresponsive nodes under the framework of NC structured DSS. In particular, the storage nodes adopt combination property with zigzag decodable (CP-ZD) storage code since it has the advantage of extremely low decoding complexity, which is promised by zigzag decoding (ZD) within a binary field. We design a v-robust PIR scheme with its download communication cost slightly larger than existing studies, but its decoding complexity is significantly reduced when compared with existing studies.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Capacity of Private Linear Computation for Coded Databases

Obead

Lin

Rosnes

et al. 2018

2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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We consider the problem of private linear computation (PLC) in a distributed storage system. In PLC, a user wishes to compute a linear combination of f messages stored in noncolluding databases while revealing no information about the coefficients of the desired linear combination to the databases. In extension of our previous work we employ linear codes to encode the information on the databases. We show that the PLC capacity, which is the ratio of the desired linear function size and the total amount of downloaded information, matches the maximum distance separable (MDS) coded capacity of private information retrieval for a large class of linear codes that includes MDS codes. In particular, the proposed converse is valid for any number of messages and linear combinations, and the capacity expression depends on the rank of the coefficient matrix obtained from all linear combinations.

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Achieving Maximum Distance Separable Private Information Retrieval Capacity With Linear Codes

Cited by 104 publications

References 47 publications

Private Polynomial Computation for Noncolluding Coded Databases

Private Polynomial Computation for Noncolluding Coded Databases

Robust private information retrieval for low encoding/decoding complexity distributed storage

Capacity of Private Linear Computation for Coded Databases

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