Pufferfish privacy (PP) is a generalization of differential privacy (DP), that offers flexibility in specifying sensitive information and integrates domain knowledge into the privacy definition. Inspired by the illuminating formulation of DP in terms of mutual information due to Cuff and Yu, this work explores PP through the lens of information theory. We provide an information-theoretic formulation of PP, termed mutual information PP (MI PP), in terms of the conditional mutual information between the mechanism and the secret, given the public information. We show that MI PP is implied by the regular PP and characterize conditions under which the reverse implication is also true, recovering the relationship between DP and its information-theoretic variant as a special case. We establish convexity, composability, and post-processing properties for MI PP mechanisms and derive noise levels for the Gaussian and Laplace mechanisms. The obtained mechanisms are applicable under relaxed assumptions and provide improved noise levels in some regimes. Lastly, applications to auditing privacy frameworks, statistical inference tasks, and algorithm stability are explored.

翻译：Pufferfish隐私（PP）是差分隐私（DP）的一种推广，它在定义敏感信息时具有灵活性，并将领域知识融入隐私定义中。受Cuff和Yu基于互信息对差分隐私进行启发性表述的启发，本文通过信息论的视角探索Pufferfish隐私。我们提出了一种信息论意义上的PP表述，称为互信息PP（MI PP），即根据机制与秘密之间的条件互信息（给定公共信息）来定义。研究表明，常规PP蕴含MI PP，并刻画了反向蕴含成立的条件，从而将差分隐私与其信息论变体之间的关系作为特例予以恢复。我们建立了MI PP机制的凸性、组合性与后处理性质，并推导了高斯机制与拉普拉斯机制所需的噪声水平。所获得的机制在更宽松的假设下适用，并在某些情况下提供了更优的噪声水平。最后，本文探讨了其在隐私框架审计、统计推断任务及算法稳定性方面的应用。