Kantorovich Mechanism for Pufferfish Privacy

TL;DR

This paper introduces a Kantorovich-based approach to calibrate noise in the exponential mechanism for achieving epsilon-pufferfish privacy, leveraging optimal transport plans derived from data statistics.

Contribution

It proposes a novel method using Kantorovich optimal transport to calibrate noise for pufferfish privacy, extending the exponential mechanism with relaxed conditions and Gaussian approximations.

Findings

Kantorovich optimal transport plan can calibrate noise for epsilon-pufferfish privacy.

The method reduces noise power while maintaining privacy guarantees.

Gaussian mechanism achieves delta-approximation of epsilon-pufferfish privacy.

Abstract

Pufferfish privacy achieves $\epsilon$-indistinguishability over a set of secret pairs in the disclosed data. This paper studies how to attain $\epsilon$-pufferfish privacy by exponential mechanism, an additive noise scheme that generalizes the Laplace noise. It is shown that the disclosed data is $\epsilon$-pufferfish private if the noise is calibrated to the sensitivity of the Kantorovich optimal transport plan. Such a plan can be obtained directly from the data statistics conditioned on the secret, the prior knowledge of the system. The sufficient condition is further relaxed to reduce the noise power. It is also proved that the Gaussian mechanism based on the Kantorovich approach attains the $\delta$-approximation of $\epsilon$-pufferfish privacy.