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Pure-DP Aggregation in the Shuffle Model: Error-Optimal and Communication-Efficient

Abstract

We obtain a new protocol for binary counting in the ε\varepsilon-shuffle-DP model with error O(1/ε)O(1/\varepsilon) and expected communication O~(lognε)\tilde{O}\left(\frac{\log n}{\varepsilon}\right) messages per user. Previous protocols incur either an error of O(1/ε1.5)O(1/\varepsilon^{1.5}) with Oε(logn)O_\varepsilon(\log{n}) messages per user (Ghazi et al., ITC 2020) or an error of O(1/ε)O(1/\varepsilon) with Oε(n2.5)O_\varepsilon(n^{2.5}) messages per user (Cheu and Yan, TPDP 2022). Using the new protocol, we obtained improved ε\varepsilon-shuffle-DP protocols for real summation and histograms.

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