# Private information retrieval in distributed storage systems using an arbitrary linear code

@article{Kumar2017PrivateIR, title={Private information retrieval in distributed storage systems using an arbitrary linear code}, author={Siddhartha Kumar and Eirik Rosnes and Alexandre Graell i Amat}, journal={2017 IEEE International Symposium on Information Theory (ISIT)}, year={2017}, pages={1421-1425} }

We propose an information-theoretic private information retrieval (PIR) scheme for distributed storage systems where data is stored using a linear systematic code of rate R> 1/2. The proposed scheme generalizes the PIR scheme for data stored using maximum distance separable codes recently proposed by Tajeddine and El Rouayheb for the scenario of a single spy node. We further propose an algorithm to optimize the communication price of privacy (cPoP) using the structure of the underlying linear…

## 54 Citations

Achieving Private Information Retrieval Capacity in Distributed Storage Using an Arbitrary Linear Code

- Computer Science, MathematicsArXiv
- 2017

This work provides a sufficient and a necessary condition for a code to be PIR capacity-achieving and proves that cyclic codes, Reed-Muller (RM) codes, and optimal information locality local reconstruction codes achieve both the finite Pir capacity and the asymptotic PIRcapacity with Protocols 1 and 2, respectively.

On the Fundamental Limit of Private Information Retrieval for Coded Distributed Storage

- Mathematics, Computer ScienceArXiv
- 2018

It is proved that the PIR capacity is indeed equal to the MDS-PIR capacity, giving the first family of non-MDS codes for which the Pir capacity is known, and provides asymmetric PIR protocols that achieve a strictly larger PIR rate compared to existing symmetric P IR protocols.

A Capacity-Achieving PIR Protocol for Distributed Storage Using an Arbitrary Linear Code

- Computer Science, MathematicsArXiv
- 2018

It is shown that cyclic codes and Reed-Muller codes satisfy the sufficient condition and are thus PIR capacity-achieving.

Asymmetry Helps: Improved Private Information Retrieval Protocols for Distributed Storage

- Computer Science, Mathematics2018 IEEE Information Theory Workshop (ITW)
- 2018

It is proved that the PIR capacity is indeed equal to the MDS-PIR capacity, giving the first family of non-MDS codes for which the Pir capacity is known, and provides asymmetric PIR protocols that achieve a strictly larger PIR rate compared to existing symmetric P IR protocols.

Private Information Retrieval From MDS Coded Data in Distributed Storage Systems

- Computer ScienceIEEE Transactions on Information Theory
- 2018

The problem of providing privacy, in the private information retrieval (PIR) sense, to users requesting data from a distributed storage system (DSS), is considered and a information theoretic PIR scheme is constructed with low download communication cost.

Achieving Maximum Distance Separable Private Information Retrieval Capacity With Linear Codes

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2019

Three private information retrieval protocols for distributed storage systems (DSSs), where data is stored using an arbitrary linear code, are proposed and it is proved that cyclic codes, Reed–Muller codes, and a class of distance-optimal local reconstruction codes achieve both the finite and the asymptotic MDS-PIR capacity.

Private information retrieval from MDS coded data in distributed storage systems

- Computer Science, Mathematics2016 IEEE International Symposium on Information Theory (ISIT)
- 2016

This work considers the problem of providing privacy, in the private information retrieval (PIR) sense, to users requesting data from a distributed storage system (DSS), and constructs PIR schemes with low download communication cost, achieving the information theoretic limit for linear schemes.

$t$ -Private Information Retrieval Schemes Using Transitive Codes

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2019

While many PIR schemes in the literature require field sizes that grow with the number of servers and files in the system, this work focuses especially on the case of a binary base field, for which Reed–Muller codes serve as an important and explicit class of examples.

Secure and Private Information Retrieval (SAPIR) in Cloud Storage Systems

- Computer ScienceIEEE Transactions on Vehicular Technology
- 2018

An information theoretic approach to security and privacy for cloud data storage systems based on random queries is proposed that ensures that a user privately downloads its desired content without the servers knowing the requested content index.

Private Information Retrieval from Coded Databases with Colluding Servers

- Computer Science, MathematicsSIAM J. Appl. Algebra Geom.
- 2017

We present a general framework for Private Information Retrieval (PIR) from arbitrary coded databases, that allows one to adjust the rate of the scheme according to the suspected number of colluding…

## References

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Private information retrieval from MDS coded data in distributed storage systems

- Computer Science, Mathematics2016 IEEE International Symposium on Information Theory (ISIT)
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This work considers the problem of providing privacy, in the private information retrieval (PIR) sense, to users requesting data from a distributed storage system (DSS), and constructs PIR schemes with low download communication cost, achieving the information theoretic limit for linear schemes.

Private Information Retrieval from Coded Databases with Colluding Servers

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We present a general framework for Private Information Retrieval (PIR) from arbitrary coded databases, that allows one to adjust the rate of the scheme according to the suspected number of colluding…

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It is proved that the tradeoff between storage cost and retrieval/download cost depends on the number of data records in the system, and proposes a class of linear storage codes and retrieval schemes, and derives conditions under which these schemes are error-free and private.

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This paper designs an explicit erasure code and PIR algorithm that requires only one extra bit of download to provide perfect privacy, and establishes the precise capacity of PIR with respect to the metric of download.

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It is proved that all known k-server PIR protocols can be efficiently emulated, while preserving both privacy and communication complexity but significantly reducing the storage overhead, and a new kind of binary linear codes are introduced, called here k- server PIR codes.

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Private Information Retrieval (PIR) protocols allow a user to retrieve a data item from a database while hiding the identity of the item being retrieved. Specifically, in information-theoretic,…

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The complexity of information-theoretic k-server PIR is improved to n/sup O(log log k/k log k)/, and the PIR protocols are more efficient than previous ones for every k/spl ges/3, and the locally decodable codes are shorter for everyk/splges/4.

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This work demonstrates the usefulness of batch codes by presenting two types of applications: trading maximal load for storage in certain load-balancing scenarios, and amortizing the computational cost of private information retrieval (PIR) and related cryptographic protocols.

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To flexibly explore the trade-offs between storage space and access efficiency in reliable data storage systems, we describe two classes of erasure resilient coding schemes: basic and generalized…

Private information retrieval

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This work describes schemes that enable a user to access k replicated copies of a database and privately retrieve information stored in the database, so that each individual server gets no information on the identity of the item retrieved by the user.