Discrete Offset-Symmetric Gaussians for Differential Privacy
Mehdi Korki, Parastoo Sadeghi · IEEE Signal Processing Letters · 2024
In many applications of differential privacy (DP), continuous distributions such as the Laplace or the Gaussian are employed to perturb data queries. However, continuous distributions are not particularly suitable for discrete data and their quantization can compromise the privacy guarantees of DP. In this letter, we extend a recently proposed continuous mechanism for DP called offset-symmetric Gaussian tail (OSGT) distribution to its discrete version, which we call DOSGT. Our findings demonstrate that the one-dimensional DOSGT mechanism achieves the same level of$(\varepsilon, \delta (\varepsilon))$-DP as the continuous OSGT, which is better than what is achievable by the discrete Gaussian at the same variance. We also derive the Rényi differential privacy (RDP) of the DOSGT mechanism. We then present a simple and efficient algorithm for accurately sampling from DOSGT distribution, showcasing its applicability in DP scenarios involving integer-valued queries.