On the Leaky Private Information Retrieval with Side Information
Yingying Huangfu, Tian Bai
TL;DR
The paper addresses private information retrieval with side information under controlled privacy leakage by introducing a unified probabilistic framework that characterizes how leakage, side information and retrieval efficiency interact. It develops explicit download-cost bounds under two leaky privacy notions, $W$-privacy and $(W,S)$-privacy, showing how the bounds converge to known PIR-SI capacities as $\varepsilon\to0$ or to leaky-PIR limits when side information is absent. The achievability relies on a randomized query framework that partitions messages into sub-packets and uses a random pattern to coordinate per-server sums, enabling correct decoding while controlling leakage. These results provide theoretical guidance for designing practical, leakage-tolerant private retrieval schemes with side information in multi-server settings.
Abstract
This paper investigates the problem of leaky-private Private Information Retrieval with Side Information (L-PIR-SI), which relaxes the requirement of perfect privacy to achieve improved communication efficiency in the presence of side information. While the capacities of PIR-SI under both $W$-privacy and $(W,S)$-privacy have been partially explored, the impact of controlled information leakage in these settings remains unaddressed. We propose a unified probabilistic framework to construct L-PIR-SI schemes where the privacy leakage is quantified by a parameter $\varepsilon$, consistent with differential privacy standards. We characterize the achievable download costs and show that our results generalize several landmark results in the PIR literature: they recover the capacity of PIR-SI when $\varepsilon \to 0$, and reduce to the known bounds for leaky-PIR when side information is absent. This work provides the first look at the trade-offs between leakage, side information, and retrieval efficiency.