Necessary and Sufficient Conditions for Capacity-Achieving Private Information Retrieval with Non-Colluding and Colluding Servers

Fuente: arXiv
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Main Authors: Miki, Atsushi, Morishita, Yusuke, Matsushima, Toshiyasu
Format: Preprint
Published: 2024
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author Miki, Atsushi
Morishita, Yusuke
Matsushima, Toshiyasu
author_facet Miki, Atsushi
Morishita, Yusuke
Matsushima, Toshiyasu
contents Private Information Retrieval (PIR) is a mechanism for efficiently downloading messages while keeping the index secret. Here, PIRs in which servers do not communicate with each other are called standard PIRs, and PIRs in which some servers communicate with each other are called colluding PIRs. The information-theoretic upper bound on efficiency has been given in previous studies. However, the conditions for PIRs to keep privacy, to decode the desired message, and to achieve that upper bound have not been clarified in matrix form. In this paper, we prove the necessary and sufficient conditions for the properties of standard PIR and colluding PIR. Further, we represent the properties in matrix form.
format Preprint
id arxiv_https___arxiv_org_abs_2404_13624
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Necessary and Sufficient Conditions for Capacity-Achieving Private Information Retrieval with Non-Colluding and Colluding Servers
Miki, Atsushi
Morishita, Yusuke
Matsushima, Toshiyasu
Information Theory
Private Information Retrieval (PIR) is a mechanism for efficiently downloading messages while keeping the index secret. Here, PIRs in which servers do not communicate with each other are called standard PIRs, and PIRs in which some servers communicate with each other are called colluding PIRs. The information-theoretic upper bound on efficiency has been given in previous studies. However, the conditions for PIRs to keep privacy, to decode the desired message, and to achieve that upper bound have not been clarified in matrix form. In this paper, we prove the necessary and sufficient conditions for the properties of standard PIR and colluding PIR. Further, we represent the properties in matrix form.
title Necessary and Sufficient Conditions for Capacity-Achieving Private Information Retrieval with Non-Colluding and Colluding Servers
topic Information Theory
url https://arxiv.org/abs/2404.13624