Spreading the Privacy Blanket: - Differentially Oblivious Shuffling for Differential Privacy

S. Dov Gordon, Jonathan Katz, Mingyu Liang, Jiayu Xu

Abstract: In the shuffle model for differential privacy, n users locally randomize their data and submit the results to a trusted “shuffler” who mixes the results before sending them to a server for analysis. This is a promising model for real-world applications of differential privacy, as several recent results have shown that, in some cases, the shuffle model offers a strictly better privacy/utility tradeoff than what is possible in a purely local model. A downside of the shuffle model is its reliance on a trusted shuffler, and it is natural to try to replace this with a distributed shuffling protocol run by the users themselves. While it would of course be possible to use a fully secure shuffling protocol, one might hope to instead use a more-efficient protocol having weaker security guarantees. In this work, we consider a relaxation of secure shuffling called differential obliviousness that we prove suffices for differential privacy in the shuffle model. We also propose a differentially oblivious shuffling protocol based on onion routing that requires only $$O(n \log n)$$ communication while tolerating any constant fraction of corrupted users. We show that for practical settings of the parameters, our protocol outperforms existing solutions to the problem.