Private Information Retrieval from Coded Storage Systems with Colluding, Byzantine, and Unresponsive Servers

TL;DR

This paper presents a new PIR scheme for coded storage systems that is resilient to colluding, byzantine, and unresponsive servers, achieving near-capacity rates especially when the storage code dimension is one.

Contribution

It introduces an explicit Reed-Solomon based PIR scheme that handles multiple server adversities and adapts to symmetric PIR, improving robustness and efficiency.

Findings

Achieves PIR rate of (n-r-(k+2b+t-1))/(n-r)

Asymptotically capacity-achieving for k=1 as number of files grows

Effective against collusion, Byzantine faults, and unresponsive servers

Abstract

The problem of Private Information Retrieval (PIR) from coded storage systems with colluding, byzantine, and unresponsive servers is considered. An explicit scheme using an $[n,k]$ Reed-Solomon storage code is designed, protecting against $t$-collusion and handling up to $b$ byzantine and $r$ unresponsive servers, when $n>k+t+2b+r-1$. This scheme achieves a PIR rate of $\frac{n-r-(k+2b+t-1)}{n-r}$. In the case where the capacity is known, namely when $k=1$, it is asymptotically capacity-achieving as the number of files grows. Lastly, the scheme is adapted to symmetric PIR.