Secure messaging groups in applications such as Signal, Telegram, and Whatsapp are nowadays used for rapid and widespread dissemination of information to large groups of people. This is common even in sensitive contexts, involving the organisation of protests, activist groups, and internal company dialogues, for instance. Manual administration of who has access to such groups quickly becomes infeasible, in the presence of even hundreds of members. We construct a practical, privacy-preserving reputation protocol, that automates the approval of new group members based on their reputation amongst the existing membership. We prove security against malicious adversaries in a single-server model, with no further trust assumptions required, while supporting arbitrary reputation calculations even when almost all group members are offline (as is likely). We demonstrate the practicality of the approach experimentally: for groups of size 50 (resp. 500), admitting a user that received 40 (resp. 80) scores requires 1312.2~KiB (resp. 13086.3~KiB) of communication, and 3.4~s (resp. 42.3~s) of single-threaded computation. While our protocol design matches existing secure messaging applications, we believe it can have value in distributed reputation computation beyond this problem setting.

We study the security of Probabilistic Data Structures (PDS) for handling Approximate Membership Queries (AMQ); prominent examples of AMQ-PDS are Bloom and Cuckoo filters. AMQ-PDS are increasingly being deployed in environments where adversaries can gain benefit from carefully selecting inputs, for example to increase the false positive rate of an AMQ-PDS. They are also being used in settings where the inputs are sensitive and should remain private in the face of adversaries who can access an AMQ-PDS through an API or who can learn its internal state by compromising the system running the AMQ-PDS.