OPERA: Reasoning about continuous common knowledge in asynchronous distributed systems

This paper introduces a new family of consensus protocols, namely \emph{Lachesis-class} denoted by $\mathcal{L}$, for distributed networks with guaranteed Byzantine fault tolerance. Each Lachesis protocol $L$ in $\mathcal{L}$ has complete asynchrony, is leaderless, has no round robin, no proof-of-work, and has eventual consensus. The core concept of our technology is the \emph{OPERA chain}, generated by the Lachesis protocol. In the most general form, each node in Lachesis has a set of $k$ neighbours of most preference. When receiving transactions a node creates and shares an event block with all neighbours. Each event block is signed by the hashes of the creating node and its $k$ peers. The OPERA chain of the event blocks is a Directed Acyclic Graph (DAG); it guarantees practical Byzantine fault tolerance (pBFT). Our framework is then presented using Lamport timestamps and concurrent common knowledge. Further, we present an example of Lachesis consensus protocol $L_0$ of our framework. Our $L_0$ protocol can reach consensus upon 2/3 of all participants' agreement to an event block without any additional communication overhead. $L_0$ protocol relies on a cost function to identify $k$ peers and to generate the DAG-based OPERA chain. By creating a binary flag table that stores connection information and share information between blocks, Lachesis achieves consensus in fewer steps than pBFT protocol for consensus.