Private, Efficient, and Optimal K-Norm and Elliptic Gaussian Noise For Sum, Count, and Vote

arXiv:2309.15790v2 Announce Type: replace
Abstract: Differentially private computation often begins with a bound on some $d$-dimensional statistic's $\ell_p$ sensitivity. For pure differential privacy, the $K$-norm mechanism can improve on this approach using statistic-specific (and possibly non-$\ell_p$) norms. However, sampling such mechanisms requires sampling from the corresponding norm balls. These are $d$-dimensional convex polytopes, for which the fastest known general sampling algorithm takes time $\tilde O(d^{3+\omega})$, where $\omega \geq 2$ is the matrix multiplication exponent. For concentrated differential privacy, elliptic Gaussian …

arxiv can computation cs.cr differential privacy elliptic mechanism noise non privacy private statistic vote