Collecting anonymous opinions has applications from whistleblowing to complex voting, where participants rank candidates by order of preference. Unfortunately, as far as we know, there is no efficient distributed solution to this problem. Previous solutions either require trusted third parties, are inefficient or sacrifice anonymity.

In this paper, we propose a distributed solution called the Anonymised Vector Consensus Protocol (AVCP) that reduces the problem of agreeing on a set of anonymous votes to the binary Byzantine consensus problem. The key idea to preserve the anonymity of voters—despite some of them act-ing maliciously—is to detect double votes through traceable ring signatures. AVCP is resilient-optimal as it tolerates up to a third of Byzantine participants.

We prove our algorithm correct and show that it preserves anonymity with, at most, linear communication overhead and constant message overhead when compared to a recent consensus baseline.

Finally, we demonstrate empirically that the protocol is practical by deploying it on 100 machines geo-distributed in three continents: America, Asia and Europe. Anonymous decisions are reached within 10 seconds with a conservative choice of traceable ring signatures.