Andrzej Wąsowski will present recent work on quantifying information leakage in probabilistic programs using Gaussian mixture semantics. This is joint work with Francesca Randone (TU Wien) and Raúl Pardo (ITU).
SPEAKER: Andrzej Wąsowski, prof. at ITU.
TITLE: Approximating Quantitative Information Flow with Gaussian-Mixtures
ABSTRACT: We propose a program analysis method to symbolically quantify information leakage, using a Gaussian mixture-based approximation semantics for probabilistic programs. Our method computes exact analytical solutions as well as upper and lower bounds for two broad classes of leakage metrics: (i) entropy-based measures and (ii) g-vulnerability metrics. For g-vulnerability, we propose two gain functions generalizing Bayes vulnerability, deriving exact expressions for Gaussian joints and sound bounds for Gaussian mixtures. To increase expressiveness, we extend the semantics of our probabilistic programming language with i.i.d. loops, enabling the encoding of rejection-sampling procedures used in practical implementations of privacy protection mechanisms. To support empirical evaluation, we extend an existing black-box estimation technique from the discrete to the continuous case. We evaluate multiple case studies that include privacy protection mechanisms used to ensure differential privacy and geo-indistinguishability, showing that our method’s results are precise and consistent with numerical estimations, but come with a symbolic, not statistical, interpretation. In particular, they are guaranteed to be sound approximations for the class of programs over Gaussian mixtures.