Cordial Miners: A Family of Simple, Efficient and Self-Contained Consensus Protocols for Every Eventuality

Cordial Miners is a family of simple, efficient, self-contained, Byzantine Atomic Broadcast protocols, with optimal instances for asynchrony and eventual synchrony. Its simplicity-cum-efficiency stems from using the blocklace -- a partially-ordered generalization of the totally-ordered blockchain -- for all key algorithmic tasks, including block dissemination, equivocation exclusion, leader finality, block ordering, and for the identification and exclusion of faulty miners. The algorithm employs piecemeal topological sort of the partially-ordered blocklace into a totally-ordered sequence of blocks, excluding equivocations as well as the Byzantine miners perpetrating them along the way. The conversion process is monotonic in that the output sequence only extends as the input blocklace increases, which implies (i) safety -- the outputs of two correct miners are consistent (one is a prefix of the other), and (ii) finality -- any output of a correct miner is final. We present two instances of the protocol family: One for the eventual synchrony model, employing deterministic/predicted leader selection and 3 rounds of communication to leader finality in the good case, which is three-quarters of the latency of state-of-the-art protocols. The second for the asynchrony model, employing retroactive random leader selection, 6 rounds to leader finality in the good case, and 9 rounds in the expected case, which is half the latency of state-of-the-art protocols in the good case and three-quarters of their latency in the expected case. In both protocols, message complexity is the same as the state-of-the-art.