International Association
for Cryptologic Research

In the shuffle model for differential privacy, users locally randomize their data and then submit the results to a trusted ``shuffler'' who mixes the responses before sending them to a server for analysis. This is a promising model for real-world applications of differential privacy, as a series of 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. The recent ``privacy blanket'' notion provides a simple method for analyzing differentially private protocols in the shuffle model.

A downside of the shuffle model is its reliance on a trusted shuffling mechanism, and it is natural to try to replace this with a distributed shuffling protocol run by the users themselves. Unfortunately, with only one exception, existing fully secure shuffling protocols require $\Omega(n^2)$ communication. In this work, we put forth a notion of differential obliviousness for shuffling protocols, and prove that this notion provides the necessary guarantees for the privacy blanket, without requiring a trusted shuffler. We also show a differentially oblivious shuffling protocol based on onion routing that can tolerate any constant fraction of corrupted users and requires only $O(n \log n)$ communication.