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

28 May 2023
Badih Ghazi
Ravi Kumar
Pasin Manurangsi
    FedML
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Abstract

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

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