Dithered Gaussian Mechanism for Randomness-Efficient Differential Privacy
For differential privacy practitioners, this provides a randomness-efficient and secure alternative to discrete Gaussian mechanisms, addressing floating-point vulnerabilities.
The dithered Gaussian mechanism discretizes the private output rather than the noise distribution, inheriting privacy guarantees of the standard Gaussian mechanism while avoiding floating-point vulnerabilities. It reduces high-quality random bits needed for privacy, making cryptographically secure noise generation feasible with modest overhead in DP-SGD.
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.