# On the Optimal File Size of Capacity-Achieving Byzantine-Resistant Private Information Retrieval Schemes

## TL;DR

This paper explores how to design efficient private information retrieval systems that resist server collusion and errors while minimizing download costs and file size.

## Contribution

The paper introduces PIR schemes with minimal download costs and smallest file size, adaptable to varying numbers of participating servers.

## Key findings

- PIR schemes with minimal download costs and smallest file size are proposed.
- A scheme is introduced that adapts to varying numbers of participating servers.
- The results extend previous conference findings to handle straggler servers.

## Abstract

We consider the problem of designing a Private Information Retrieval (PIR) scheme for n files replicated on k servers that can collude and return incorrect answers. Our goal is to correctly retrieve a specific message while keeping its identity private from the database servers. We focus on minimizing download costs and propose PIR schemes with minimal download costs and the smallest file size (proportional to the number of involved servers). Motivated by the possible presence of stragglers, we extend our previous conference results and propose a scheme in which the number of participating servers may vary.