We obtain a new protocol for binary counting in the $\varepsilon$-shuffle-DP model with error $O(1/\varepsilon)$ and expected communication $\tilde{O}\left(\frac{\log n}{\varepsilon}\right)$ messages per user. Previous protocols incur either an error of $O(1/\varepsilon^{1.5})$ with $O_\varepsilon(\log{n})$ messages per user (Ghazi et al., ITC 2020) or an error of $O(1/\varepsilon)$ with $O_\varepsilon(n^{2.5})$ messages per user (Cheu and Yan, TPDP 2022). Using the new protocol, we obtained improved $\varepsilon$-shuffle-DP protocols for real summation and histograms.

翻译：我们提出了一种$\varepsilon$-shuffle-DP模型下二进制计数的新协议，其误差为$O(1/\varepsilon)$，每个用户期望通信量为$\tilde{O}\left(\frac{\log n}{\varepsilon}\right)$条消息。现有协议要么每个用户需传输$O_\varepsilon(\log{n})$条消息但误差为$O(1/\varepsilon^{1.5})$（Ghazi等，ITC 2020），要么每个用户需传输$O_\varepsilon(n^{2.5})$条消息但误差为$O(1/\varepsilon)$（Cheu和Yan，TPDP 2022）。利用该新协议，我们进一步改进了实数求和与直方图问题的$\varepsilon$-shuffle-DP协议。