Analysis of the Matrix Event Graph Replicated Data Type

Matrix is a new kind of decentralized, topic-based publish-subscribe middleware for communication and data storage that is getting particularly popular as a basis for secure instant messaging. By comparison with traditional decentralized communication systems, Matrix replaces pure message passing with a replicated data structure. This data structure, which we extract and call the Matrix Event Graph (MEG), depicts the causal history of messages. We show that this MEG represents an interesting and important replicated data type for decentralized applications that are based on causal histories of publish-subscribe events: First, we prove that the MEG is a Conflict-Free Replicated Data Type for causal histories and, thus, provides Strong Eventual Consistency (SEC). With SEC being among the best known achievable trade-offs in the scope of the well-known CAP theorem, the MEG provides a powerful consistency guarantee while being available during network partition. Second, we discuss the implications of byzantine attackers on the data type's properties. We note that the MEG, as it does not strive for consensus or strong consistency, can cope with n > f environments with n participants, of which f are byzantine. Furthermore, we analyze scalability: Using Markov chains, we study the number of forward extremities of the MEG over time and observe an almost optimal evolution. We conjecture that this property is inherent to the underlying spatially inhomogeneous random walk. With the properties shown, a MEG represents a promising element in the set of data structures for decentralized applications, but with distinct trade-offs compared to traditional blockchains and distributed ledger technologies.