Private Information Retrieval from Coded Databases with Colluding Servers

TL;DR

This paper introduces a flexible framework for private information retrieval from coded databases that can be adjusted to protect against varying numbers of colluding servers, achieving optimal rates in large databases.

Contribution

It develops a general PIR scheme for coded databases that adapts to the number of colluding servers and attains known capacity bounds asymptotically.

Findings

Achieves PIR rate 1-(k+t-1)/n for all t between 1 and n-k.

Interpolates between known cases of t=1 and k=1.

As database size grows, approaches the capacity bounds.

Abstract

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 servers. If the storage code is a generalized Reed-Solomon code of length n and dimension k, we design PIR schemes which simultaneously protect against t colluding servers and provide PIR rate 1-(k+t-1)/n, for all t between 1 and n-k. This interpolates between the previously studied cases of t=1 and k=1 and asymptotically achieves the known capacity bounds in both of these cases, as the size of the database grows.