Symbolic Quantitative Information Flow for Probabilistic Programs

Abstract

It is of utmost importance to ensure that modern data intensive systems do not leak sensitive information. In this paper, the authors, who met thanks to Joost-Pieter Katoen, discuss symbolic methods to compute information-theoretic measures of leakage: entropy, conditional entropy, Kullback-Leibler divergence, and mutual information. We build on two semantic frameworks for symbolic execution of probabilistic programs. For discrete programs, we use weakest pre-expectation calculus to compute exact symbolic expressions for the leakage measures. Using Second Order Gaussian Approximation (SOGA), we handle programs that combine discrete and continuous distributions. However, in the SOGA setting, we approximate the exact semantics using Gaussian mixtures and compute bounds for the measures. We demonstrate the use of our methods in two widely used mechanisms to ensure differential privacy: randomized response and the Gaussian mechanism.

Pre-print of paper appearing in "In Principles of Verification: Cycling the Probabilistic Landscape-Essays Dedicated to Joost-Pieter Katoen on the Occasion of His 60th Birthday, 2024" (https://doi.org/10.1007/978-3-031-75783-9_6)

References in corpus (8)

• Quantitative Separation Logic - A Logic for Reasoning about Probabilistic Programs
• F-BLEAU: Fast Black-box Leakage Estimation
• A Deductive Verification Infrastructure for Probabilistic Programs (Extended Version)
• Flexible and scalable privacy assessment for very large datasets, with an application to official governmental microdata
• Hybrid Statistical Estimation of Mutual Information and its Application to Information Flow
• Bounding Information Leakage in Machine Learning
• Inference of Probabilistic Programs with Moment-Matching Gaussian Mixtures
• A Quantitative Information Flow Analysis of the Topics API