Pufferfish privacy achieves $ε$-indistinguishability over a set of secret pairs in the disclosed dataset. This paper studies how to attain pufferfish privacy by the exponential mechanism, an additive noise scheme that generalizes Gaussian and Laplace noise. A sufficient condition is derived showing that pufferfish privacy is attained by calibrating noise to the sensitivity of the Kantorovich optimal transport plan. Such a plan can be directly computed by using the data statistics conditioned on

more »

... the secret, the prior knowledge about the system. It is shown that Gaussian noise provides better data utility than Laplace noise when the privacy budget $ε$ is small. The sufficient condition is then relaxed to reduce the noise power. Experimental results show that the relaxed sufficient condition improves data utility of the pufferfish private data regulation schemes.