Privacy-Aware Rejection Sampling

Abstract

Differential privacy (DP) offers strong theoretical privacy guarantees, but implementations of DP mechanisms may be vulnerable to side-channel attacks, such as timing attacks. When sampling methods such as MCMC or rejection sampling are used to implement a mechanism, the runtime can leak private information. We characterize the additional privacy cost due to the runtime of a rejection sampler in terms of both $(\epsilon ,\delta )$-DP as well as $f$-DP. We also show that unless the acceptance probability is constant across databases, the runtime of a rejection sampler does not satisfy $\epsilon$-DP for any $\epsilon$. We show that there is a similar breakdown in privacy with adaptive rejection samplers. We propose three modifications to the rejection sampling algorithm, with varying assumptions, to protect against timing attacks by making the runtime independent of the data. The modification with the weakest assumptions is an approximate sampler, introducing a small increase in the privacy cost, whereas the other modifications give perfect samplers. We also use our techniques to develop an adaptive rejection sampler for log-Hölder densities, which also has data-independent runtime. We give several examples of DP mechanisms that fit the assumptions of our methods and can thus be implemented using our samplers.

25 pages + references, 4 figures

References in corpus (5)

• Privacy Loss in Apple's Implementation of Differential Privacy on MacOS 10.12
• Gaussian Differential Privacy
• Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo
• Benefits and Pitfalls of the Exponential Mechanism with Applications to Hilbert Spaces and Functional PCA
• Near Instance-Optimality in Differential Privacy