End-to-end (E2E) encryption is now widely deployed in messaging apps such as WhatsApp and Signal and billions of people around the world have the contents of their message protected against strong adversaries. However, while the message contents are encrypted, their metadata still leaks sensitive information. For example, it is easy for an infrastructure provider to tell which customers are communicating, with whom and when.

Anonymous communication hides this metadata. This is crucial for the protection of individuals such as whistleblowers who expose criminal wrongdoing, activists organising a protest, or embassies coordinating a response to a diplomatic incident. All these face powerful adversaries for whom the communication metadata alone (without knowing the specific message text) can result in harm for the individuals concerned.

Tor is a popular tool that achieves anonymous communication by forwarding messages through multiple intermediate nodes or relays. At each relay the outermost layer of the message is decrypted and the inner message is forwarded to the next relay. An adversary who wants to figure out where A’s messages are finally delivered can attempt to follow a message as it passes through each relay. Alternatively, an adversary might confirm a suspicion that user A talks to user B by observing traffic patterns at A’s and B’s access points to the network instead. If indeed A and B are talking to each other, there will be a correlation between their traffic patterns. For instance, if an adversary observes that A sends three messages and three messages arrive at B shortly afterwards, this provides some evidence that A talks to B. The adversary can increase their certainty by collecting traffic over a longer period of time.

Mix networks such as Loopix use a different design, which defends against such traffic analysis attacks by using (i) traffic shaping and (ii) more intermediate nodes, so called mix nodes. In a simple mix network, each client only sends packets of a fixed length and at predefined intervals (e.g. 1 KiB every 5 seconds). When there is no payload to send, a cover packet is crafted that is indistinguishable to the adversary from a payload packet. If there is more than one payload packet to be sent, packets are queued and sent one by one on the predefined schedule. This traffic shaping ensures that an observer cannot gain any information from observing outgoing network packets. Moreover, mix nodes typically delay each incoming message by a random amount of time before forwarding it (with the delay chosen independently for each message), making it harder for an adversary to correlate a mix node’s incoming and outgoing messages, since they are likely to be reordered. In contrast, Tor relays forward messages as soon as possible in order to minimise latency.

Mix Networks work well for pairwise communication, but we found that group communication creates a unique challenge. Such group communication encompasses both traditional chat groups (e.g. WhatsApp groups or IRC) and collaborative editing (e.g. Google Docs, calendar sync, todo lists) where updates need to be disseminated to all other participants who are viewing or editing the content. There are many scenarios where anonymity requirements meet group communication, such as coordination between activists, diplomatic correspondence between embassies, and organisation of political campaigns.

The traffic shaping of mix networks makes efficient group communication difficult. The limited rate of outgoing messages means that sequentially sending a message to each group member can take a long time. For instance, assuming that the outgoing rate is 1 message every 5 seconds, it will take more than 8 minutes to send the message to all members in a group of size 100. During this process the sender’s output queue is blocked and they cannot send any other messages.

In our paper we propose a scheme named Rollercoaster that greatly improves the latency for group communication in mix networks. The basic idea is that group members who have already received a message can help distribute it to other members of the group. Like a chain reaction, the distribution of the message gains momentum as the number of recipients grows. In an ideal execution of this scheme, the number of users who have received a message doubles with every round, leading to substantially more efficient message delivery across the group.

Rollercoaster works well because there is typically plenty of spare capacity in the network. At any given time most clients will not be actively communicating and they are therefore mostly sending cover traffic. As a result, Rollercoaster actually improves the efficiency of the network and reduces the rate of cover traffic, which in turn reduces the overall required network bandwidth. At the same time, Rollercoaster does not require any changes to the existing Mix network protocol and can benefit from the existing user base and anonymity set.

The basic idea requires more careful consideration in a realistic environment where clients are offline or do not behave faithfully. A fault-tolerant version of our Rollercoaster scheme addresses these concerns by waiting for acknowledgement messages from recipients. If those acknowledgement messages are not received by the sender in a fixed period of time, forwarding roles are reassigned and another delivery attempt is made via a new route. We also show how a single number can seed the generation of a deterministic forwarding schedule. This allows efficient communication of different forwarding schedules and balances individual workloads within the group.

We presented our paper at USENIX Security ‘21 (paper, slides, and recording). It contains more extensions and optimisations than we can summarise here. There is also an extended version available as a tech report with more detailed security arguments in the appendices. The paper reference is:
Daniel Hugenroth, Martin Kleppmann, and Alastair R. Beresford. Rollercoaster: An Efficient Group-Multicast Scheme for Mix Networks. Proceedings of the 30th USENIX Security Symposium (USENIX Security), 2021.