Optimizing Leaky Private Information Retrieval Codes to Achieve ${O}(\log K)$ Leakage Ratio Exponent

TL;DR

This paper proposes an optimized probabilistic scheme for leaky private information retrieval that significantly reduces privacy leakage, achieving an ${O}(\log K)$ exponent compared to the previous $ heta(K)$, with fixed download cost.

Contribution

It introduces a joint probability optimization for retrieval patterns, revealing a layered structure that improves privacy leakage bounds in L-PIR.

Findings

Achieves ${O}(\log K)$ leakage ratio exponent with fixed download cost.

Optimizes retrieval pattern probabilities jointly, not just selectively.

Demonstrates a layered probability distribution structure for patterns.

Abstract

We study the problem of leaky private information retrieval (L-PIR), where the amount of privacy leakage is measured by the pure differential privacy parameter, referred to as the leakage ratio exponent. Unlike the previous L-PIR scheme proposed by Samy et al., which only adjusted the probability allocation to the clean (low-cost) retrieval pattern, we optimize the probabilities assigned to all the retrieval patterns jointly. It is demonstrated that the optimal retrieval pattern probability distribution is quite sophisticated and has a layered structure: the retrieval patterns associated with the random key values of lower Hamming weights should be assigned higher probabilities. This new scheme provides a significant improvement, leading to an ${O}(\log K)$ leakage ratio exponent with fixed download cost $D$ and number of servers $N$, in contrast to the previous art that only achieves a $\Theta(K)$ exponent, where $K$ is the number of messages.