dc.contributor.author | Martínez Peñas, Umberto | |
dc.date.accessioned | 2024-12-20T10:33:30Z | |
dc.date.available | 2024-12-20T10:33:30Z | |
dc.date.issued | 2024 | |
dc.identifier.citation | Finite Fields and Their Applications, junio 2024, vol. 96, 102421 | es |
dc.identifier.issn | 1071-5797 | es |
dc.identifier.uri | https://uvadoc.uva.es/handle/10324/72945 | |
dc.description | Producción Científica | es |
dc.description.abstract | We consider information-theoretical private information retrieval (PIR) from a coded database with colluding servers.
We target, for the first time, locally repairable storage codes
(LRCs). We consider any number of local groups g, locality
r, local distance δ and dimension k. Our main contribution is
a PIR scheme for maximally recoverable (MR) LRCs based
on linearized Reed–Solomon codes, which achieve the smallest field sizes among MR-LRCs for many parameter regimes.
In our scheme, nodes are identified with codeword symbols
and servers are identified with local groups of nodes. Only
locally non-redundant information is downloaded from each
server, that is, only r nodes (out of r + δ − 1) are downloaded per server. The PIR scheme achieves the (download)
rate R = (N −k−rt+1)/N, where N = gr is the length of the
MDS code obtained after removing the local parities, and for
any t colluding servers such that k+rt ≤ N. For an unbounded
number of stored files, the obtained rate is strictly larger than
those of known PIR schemes that work for any MDS code.
Finally, the obtained PIR scheme can also be adapted when
communication between the user and each server is performed
via linear network coding, achieving the same rate as previous PIR schemes for this scenario but with polynomial finite
field sizes, instead of exponential. Our rates are equal to those
of PIR schemes for Reed–Solomon codes, but Reed–Solomon
codes are incompatible with the MR-LRC property or linear
network coding, thus our PIR scheme is less restrictive in its
applications. | es |
dc.format.mimetype | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Elsevier | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
dc.subject.classification | Distributed storage | es |
dc.subject.classification | Linearized Reed-Solomon codes | es |
dc.subject.classification | Locally repairable codes | es |
dc.subject.classification | Network coding | es |
dc.subject.classification | Private information retrieval | es |
dc.title | Private information retrieval from locally repairable databases with colluding servers | es |
dc.type | info:eu-repo/semantics/article | es |
dc.rights.holder | © 2024 The Author | es |
dc.identifier.doi | 10.1016/j.ffa.2024.102421 | es |
dc.relation.publisherversion | https://www.sciencedirect.com/science/article/pii/S1071579724000601 | es |
dc.identifier.publicationfirstpage | 102421 | es |
dc.identifier.publicationtitle | Finite Fields and Their Applications | es |
dc.identifier.publicationvolume | 96 | es |
dc.peerreviewed | SI | es |
dc.description.project | The Independent Research Fund Denmark (Grant No. DFF-7027-00053B) | es |
dc.rights | Atribución 4.0 Internacional | * |
dc.type.hasVersion | info:eu-repo/semantics/publishedVersion | es |