Recent work argues for using Gaussian differential privacy (GDP) to report the privacy guarantees in privacy-preserving machine learning. We provide principled mappings from pure-DP ε to GDP μ by matching the worst-case success of a strong-adversary membership inference attack in terms of three metrics: multiplicative advantage at fixed FPR, precision at fixed recall, and the standard privacy profile. We tabulate μ values across a useful range of parameters and recommend μ≈ε/5 as a conservative general-purpose conversion.
State-of-the-art Differentially Private (DP) synthetic data generators such as MST and AIM are widely used, yet tightly auditing their privacy guarantees remains challenging. We introduce a Gaussian Differential Privacy (GDP)-based auditing framework that measures privacy via the full false-positive/false-negative tradeoff. Applied to MST and AIM under worst-case settings, our method provides the first tight audits in the strong-privacy regime. For (ε,δ)=(1,10−2), we obtain μemp≈0.43 vs. implied μ=0.45, showing a small theory-practice gap. Our code is publicly available: https://github.com/sassoftware/dpmm.
Georgi Ganev, Meenatchi Sundaram Muthu Selva Annamalai, Bogdan Kulynych
We design a class of additive noise mechanisms that satisfy (ε,δ)-differential privacy (DP) for scalar, real-valued query functions with known sensitivities, with a particular focus on moderate and low-privacy regimes. These mechanisms, which we call \textit{mixture mechanisms}, are constructed by mixing multiple Gaussian distributions that share the same variance but differ in their means and mixture weights. The resulting distributions can be interpreted as convex combinations of a zero-mean Gaussian (as used in the analytic Gaussian mechanism) and additional Gaussians whose means depend on the sensitivity of the query function. We derive tight conditions on the variances required for (ε,δ)-DP and provide efficient algorithms to compute them. Compared to the analytic Gaussian mechanism, our mechanisms yield substantially lower expected noise amplitudes (l1-loss) and variances (l2-loss for zero-mean distributions). In the low-privacy regime that motivates our design, our mechanisms approach optimality, mitigating nearly all of the optimality gap of the analytic Gaussian mechanism.
We present the dithered Gaussian mechanism, a novel alternative to the discrete Gaussian mechanism for differential privacy that discretizes the private output rather than the noise distribution itself. By interpreting this discretization as post-processing of the Gaussian mechanism, our construction directly inherits the privacy guarantees of the standard Gaussian mechanism while avoiding vulnerabilities caused by finite-precision floating-point outputs. We show that the mechanism is provably randomness-efficient: by sampling the discretized output values directly, the number of high-quality random bits required for privacy can be reduced significantly and made independent of the noise level. This is achieved by separating the randomness into two sources: a high-quality source used for the privacy-critical sampling step, and a high-performance public source, possibly known to the adversary, that supplies the additional randomness needed for randomized discretization. This separation enables the use of cryptographically secure randomness without substantial performance loss. As an application, we study model training with DP-SGD and show that cryptographically secure noise generation with reduced exposure to floating-point vulnerabilities can be achieved with modest practical overhead.