Reviewing and Improving the Gaussian Mechanism for Differential Privacy

Understand

Differential privacy provides a rigorous framework to quantify data privacy, and has received considerable interest recently.

• A randomized mechanism satisfying $(\epsilon, \delta)$-differential privacy (DP) roughly means that, except with a small probability $\delta$, altering a record in a dataset cannot change the probability that an output is seen by more than a multiplicative factor $e^{\epsilon} $.
• A well-known solution to $(\epsilon, \delta)$-DP is the Gaussian mechanism initiated by Dwork et al.
• [1] in 2006 with an improvement by Dwork and Roth [2] in 2014, where a Gaussian noise amount $\sqrt{2\ln \frac{2}{\delta}} \times \frac{\Delta}{\epsilon}$ of [1] or $\sqrt{2\ln \frac{1.25}{\delta}} \times \frac{\Delta}{\epsilon}$ of [2] is added independently to each dimension of the query result, for a query with $\ell_2$-sensitivity $\Delta$.