Private Information Retrieval from MDS Coded Databases with Colluding Servers under Several Variant Models

TL;DR

This paper introduces a comprehensive PIR scheme applicable to various models involving MDS coded databases, addressing challenges like collusion, robustness, and Byzantine faults to enhance private data retrieval efficiency.

Contribution

It proposes a unified PIR scheme that handles multiple variants, including robust, Byzantine, multi-file, and arbitrary collusion models, expanding the applicability of PIR techniques.

Findings

Achieves private retrieval with arbitrary collusion patterns

Extends PIR capacity analysis to multiple variants

Provides a general scheme applicable to diverse models

Abstract

Private information retrieval (PIR) gets renewed attentions due to its information-theoretic reformulation and its application in distributed storage system (DSS). The general PIR model considers a coded database containing $N$ servers storing $M$ files. Each file is stored independently via the same arbitrary $(N,K)$-MDS code. A user wants to retrieve a specific file from the database privately against an arbitrary set of $T$ colluding servers. A key problem is to analyze the PIR capacity, defined as the maximal number of bits privately retrieved per one downloaded bit. Several extensions for the general model appear by bringing in various additional constraints. In this paper, we propose a general PIR scheme for several variant PIR models including: PIR with robust servers, PIR with Byzantine servers, the multi-file PIR model and PIR with arbitrary collusion patterns.