DeCAF: Decentralizable CGKA with Fast Healing

Continuous group key agreement (CGKA) allows a group of users to maintain a continuously updated shared key in an asynchronous setting where parties only come online sporadically and their messages are relayed by an untrusted server. CGKA captures the basic primitive underlying group messaging schemes. Current solutions including TreeKEM (“Messaging Layer Security” (MLS) IETF RFC 9420) cannot handle concurrent requests while retaining low communication complexity. The exception being CoCoA, which is concurrent while having extremely low communication complexity (in groups of size n and for m concurrent updates the communication per user is \(\log (n)\) , i.e., independent of m). The main downside of CoCoA is that in groups of size n, users might have to do up to \(\log (n)\) update requests to the server to ensure their (potentially corrupted) key material has been refreshed. In this work we present a “fast healing” concurrent CGKA protocol, named DeCAF, where users will heal after at most \(\log (t)\) requests, with t being the number of corrupted users. While also suitable for the standard central-server setting, our protocol is particularly interesting for realizing decentralized group messaging, where protocol messages (add, remove, update) are being posted on some append-only data structure rather than sent to a server. In this setting, concurrency is crucial once the rate of requests exceeds, say, the rate at which new blocks are added to a blockchain. In the central-server setting, CoCoA (the only alternative with concurrency, sub-linear communication and basic post-compromise security) enjoys much lower download communication. However, in the decentralized setting – where there is no server which can craft specific messages for different users to reduce their download communication – our protocol significantly outperforms CoCoA. DeCAF heals in fewer epochs ( \(\log (t)\) vs. \(\log (n)\) ) while incurring a similar per epoch per user communication cost.