Kantorovich Mechanism for Pufferfish Privacy
It addresses privacy concerns in data disclosure for systems with prior knowledge, but appears incremental as it builds on existing Pufferfish and exponential mechanism concepts.
This paper tackles the problem of achieving Pufferfish privacy, a framework for data privacy, by proposing a mechanism based on the Kantorovich optimal transport plan to calibrate noise, resulting in sufficient conditions for ε-pufferfish privacy and relaxed noise requirements, with extensions to Gaussian mechanisms for δ-approximation.
Pufferfish privacy achieves $ε$-indistinguishability over a set of secret pairs in the disclosed data. This paper studies how to attain $ε$-pufferfish privacy by exponential mechanism, an additive noise scheme that generalizes the Laplace noise. It is shown that the disclosed data is $ε$-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 $δ$-approximation of $ε$-pufferfish privacy.