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Decentralized payment systems such as Bitcoin have become massively popularin the last few years, yet there is still much to be done in understandingtheir formal properties. The vast majority of decentralized payment systemswork by achieving consensus on the state of the network; a natural question totherefore ask is whether this consensus is necessary. In this paper, weformally define a model of payment systems, and present two main results. InTheorem 1, we show that even though there exists a single step black boxreduction from Payment Systems to Byzantine Broadcast, there does not exist anyblack box reduction in the other direction which is significantly better than atrivial reduction. In Theorem 2, we show how to construct Payment Systems whichonly require a very small number of messages to be sent per transaction. Inparticular, global consensus about which transactions have occurred is notnecessary for payments in this model. We then show a relation between theconstruction in Theorem 2 and the Lightning Network, relating the formal modelconstructions we have given to a practical algorithm proposed by thecryptocurrency community.

Payment Does Not Imply Consensus (For Distributed Payment Systems)