Differential privacy for symmetric log-concave mechanisms
This work addresses the challenge of optimizing noise addition for privacy in data analysis, offering a more efficient method for practitioners, though it is incremental as it builds on prior conditions for Gaussian noise.
The paper tackles the problem of minimizing noise while ensuring differential privacy in database queries, extending previous work to provide a necessary and sufficient condition for symmetric log-concave noise mechanisms, which results in significantly lower mean squared errors compared to existing Laplace and Gaussian mechanisms for the same privacy parameters.
Adding random noise to database query results is an important tool for achieving privacy. A challenge is to minimize this noise while still meeting privacy requirements. Recently, a sufficient and necessary condition for $(ε, δ)$-differential privacy for Gaussian noise was published. This condition allows the computation of the minimum privacy-preserving scale for this distribution. We extend this work and provide a sufficient and necessary condition for $(ε, δ)$-differential privacy for all symmetric and log-concave noise densities. Our results allow fine-grained tailoring of the noise distribution to the dimensionality of the query result. We demonstrate that this can yield significantly lower mean squared errors than those incurred by the currently used Laplace and Gaussian mechanisms for the same $ε$ and $δ$.