Achieving Maximum Distance Separable Private Information Retrieval Capacity With Linear Codes
Artikel i vetenskaplig tidskrift, 2019

We propose three private information retrieval (PIR) protocols for distributed storage systems (DSSs) where data is stored using an arbitrary linear code. The first two protocols, named Protocol 1 and Protocol 2, achieve privacy for the scenario with noncolluding nodes. Protocol 1 requires a file size that is exponential in the number of files in the system, while Protocol 2 requires a file size that is independent of the number of files and is hence simpler. We prove that, for certain linear codes, Protocol 1 achieves the maximum distance separable (MDS) PIR capacity, i.e., the maximum PIR rate (the ratio of the amount of retrieved stored data per unit of downloaded data) for a DSS that uses an MDS code to store any given (finite and infinite) number of files, and Protocol 2 achieves the asymptotic MDS-PIR capacity (with infinitely large number of files in the DSS). In particular, we provide a necessary and a sufficient condition for a code to achieve the MDS-PIR capacity with Protocols 1 and 2 and prove that cyclic codes, Reed-Muller (RM) codes, and a class of distance-optimal local reconstruction codes achieve both the finite MDS-PIR capacity (i.e., with any given number of files) and the asymptotic MDS-PIR capacity with Protocols 1 and 2, respectively. Furthermore, we present a third protocol, Protocol 3, for the scenario with multiple colluding nodes, which can be seen as an improvement of a protocol recently introduced by Freij-Hollanti et al.. Similar to the noncolluding case, we provide a necessary and a sufficient condition to achieve the maximum possible PIR rate of Protocol 3. Moreover, we provide a particular class of codes that is suitable for this protocol and show that RM codes achieve the maximum possible PIR rate for the protocol. For all three protocols, we present an algorithm to optimize their PIR rates.

linear codes

local reconstruction codes

generalized Hamming weight

private information retrieval

distributed storage

colluding servers

Reed-Muller codes

Code automorphisms

Författare

Siddhartha Kumar

Hsuan-Yin Lin

Eirik Rosnes

Alexandre Graell i Amat

Chalmers, Elektroteknik, Kommunikations- och antennsystem, Kommunikationssystem

IEEE Transactions on Information Theory

0018-9448 (ISSN)

Distribuerad lagring för datalagring och trådlös leverans av data

Vetenskapsrådet (VR), 2016-01-01 -- 2019-12-31.

Ämneskategorier

Datorteknik

Telekommunikation

Kommunikationssystem

Styrkeområden

Informations- och kommunikationsteknik

DOI

10.1109/TIT.2019.2900313

Mer information

Senast uppdaterat

2019-03-01