Pure Differential Privacy from Secure Intermediaries
This work addresses privacy-preserving data analysis for applications requiring strong privacy guarantees, representing a significant but incremental improvement over prior methods.
The paper tackles the problem of achieving pure differential privacy with lower error in secure intermediary models, presenting a new protocol that reduces additive error from O(1/ε^{3/2}) to O(1/ε) and applies it to distribution uniformity testing with optimal sample complexity.
Recent work in differential privacy has explored the prospect of combining local randomization with a secure intermediary. Specifically, there are a variety of protocols in the secure shuffle model (where an intermediary randomly permutes messages) as well as the secure aggregation model (where an intermediary adds messages). Most of these protocols are limited to approximate differential privacy. An exception is the shuffle protocol by Ghazi, Golowich, Kumar, Manurangsi, Pagh, and Velingker (arXiv:2002.01919): it computes bounded sums under pure differential privacy. Its additive error is $\tilde{O}(1/\varepsilon^{3/2})$, where $\varepsilon$ is the privacy parameter. In this work, we give a new protocol that ensures $O(1/\varepsilon)$ error under pure differential privacy. We also show how to use it to test uniformity of distributions over $[d]$. The tester's sample complexity has an optimal dependence on $d$. Our work relies on a novel class of secure intermediaries which are of independent interest.