An Information-Theoretic Characterization of Pufferfish Privacy

Pufferfish privacy (PP) is an appealing generalization of differential privacy (DP), that offers flexibility in specifying sensitive information and integrating domain knowledge into the privacy definition. Inspired by the illuminating equivalent formulation of DP in terms of mutual information proposed by Cuff and Yu [1], this work explores PP through the lens of information theory. We provide an equivalent information-theoretic formulation of PP as the conditional mutual information between the mechanism and the secret, given the public information. This formulation lends well for an information-theoretic analysis, and we use it to prove convexity, composability, and post-processing properties for PP mechanisms. We also leverage our formulation to derive noise levels for the Gaussian PP mechanisms. The obtained mechanisms are applicable under relaxed assumptions and provide improved noise levels in some regimes, compared to existing approaches,