  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.
