The $\epsilon$-error Capacity of Symmetric PIR with Byzantine Adversaries

TL;DR

This paper investigates the capacity of symmetric private information retrieval in the presence of Byzantine adversaries, showing that allowing a small error probability and weakening the adversary's capabilities increases the retrieval capacity.

Contribution

It demonstrates that under relaxed adversary conditions and vanishing error probability, the PIR capacity improves from 1 - (T+2B)/N to 1 - (T+B)/N.

Findings

Capacity increases to 1 - (T+B)/N with relaxed adversary assumptions.

Allowing vanishing error probability improves PIR capacity.

Weakening the adversary's observation capabilities enhances retrieval efficiency.

Abstract

The capacity of symmetric private information retrieval with $K$ messages, $N$ servers (out of which any $T$ may collude), and an omniscient Byzantine adversary (who can corrupt any $B$ answers) is shown to be $1 - \frac{T+2B}{N}$ [1], under the requirement of zero probability of error. In this work, we show that by weakening the adversary slightly (either providing secret low rate channels between the servers and the user, or limiting the observation of the adversary), and allowing vanishing probability of error, the capacity increases to $1 - \frac{T+B}{N}$.