Spreading the Privacy Blanket: Differentially Oblivious Shuffling for Differential Privacy

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 the shuffle model sometimes 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 in some settings

Walking Onions: Scaling Distribution of Information Safely in Anonymity Networks

Scaling anonymity networks offers unique security challenges, as attackers can exploit differing views of the network’s topology to perform epistemic and route capture attacks. Anonymity networks in practice, such as Tor, have opted for security over scalability by requiring participants to share a globally consistent view of all relays to prevent these kinds of attacks. Such an approach requires each user to maintain up-to-date information about every relay, causing the total amount of data each user must download every epoch to scale linearly with the number of relays. As the number of clients increases, more relays must be added to provide bandwidth, further exacerbating the total load on the network. In this work, we present Walking Onions, a set of protocols improving scalability for anonymity networks. Walking Onions enables constant-size scaling of the information each user must download in every epoch, even as the number of relays in the network grows. Furthermore, we show how relaxing the clients’ bandwidth growth from constant to logarithmic can enable an outsized improvement to relays’ bandwidth costs. Notably, Walking Onions offers the same security properties as current designs that require a globally consistent network view. We present two protocol variants. The first requires minimal changes from current onion-routing systems. The second presents a more significant design change, thereby reducing the latency required to establish a path through the network while providing better forward secrecy than previous such constructions. We evaluate Walking Onions against a generalized onion-routing anonymity network and discuss tradeoffs among the approaches