3 years ago

Reasoning about Divergences for Relaxations of Differential Privacy.

Justin Hsu, Marco Gaboardi, Shin-ya Katsumata, Gilles Barthe, Tetsuya Sato

We develop a semantics framework for verifying recent relaxations of differential privacy: R\'enyi differential privacy and zero-concentrated differential privacy. Both notions require a bound on a particular statistical divergence between two probability distributions. In order to reason about such properties compositionally, we introduce approximate span-liftings, generalizing approximate relational liftings previously developed for standard differential privacy to a more general class of divergences, and to continuous distributions. To enable verification of possibly non-terminating programs, our framework supports generalized divergences between subprobability measures. As a concrete application, we use approximate span-liftings to develop a program logic that can prove relaxations of differential privacy and other probabilistic properties based on statistical

Publisher URL: http://arxiv.org/abs/1710.09010

DOI: arXiv:1710.09010v1

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