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We present DAG-Rider, the first asynchronous Byzantine Atomic Broadcast protocol that achieves optimal resilience, optimal amortized communication complexity, and optimal time complexity. DAG-Rider is post-quantum safe and ensures that all values proposed by correct processes eventually get delivered. We construct DAG-Rider in two layers: In the first layer, processes reliably broadcast their proposals and build a structured Directed Acyclic Graph (DAG) of the communication among them. In the second layer, processes locally observe their DAGs and totally order all proposals with no extra communication. CCS CONCEPTS• Theory of computation → Distributed algorithms; • Security and privacy → Distributed systems security.

The decentralized cryptocurrency Bitcoin has experienced great success but also encountered many challenges. One of the challenges has been the long confirmation time. Another challenge is the lack of incentives at certain steps of the protocol, raising concerns for transaction withholding, selfish mining, etc. To address these challenges, we propose Solida, a decentralized blockchain protocol based on reconfigurable Byzantine consensus augmented by proof-of-work. Solida improves on Bitcoin in confirmation time, and provides safety and liveness assuming the adversary control less than (roughly) one-third of the total mining power. * Solidus was a gold coin used in the Byzantine Empire. Solida is our way of (mis-)spelling Solidus. * * An earlier version of this paper contains incentive designs (https://arxiv.org/abs/1612.02916v1). This version adds rigorous analysis of safety and liveness assuming an honest supermajority. We leave rigorous analysis of incentives to future work.

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