Continuous-Time Analysis of the Bitcoin and Prism Backbone Protocols
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Bitcoin is a peer-to-peer payment system proposed by Nakamoto in 2008. Based on the Nakamoto consensus, Bagaria, Kannan, Tse, Fanti, and Viswanath proposed the Prism protocol in 2018 and showed that it achieves near-optimal blockchain throughput while maintaining similar level of security as bitcoin. This work provides the probabilistic guarantees for the liveliness and consistency of bitcoin and Prism transactions. Previous analyses of the bitcoin and Prism have been either established under a simplified discrete-time model or expressed in terms of exponential order result. This paper presents a streamlined and strengthened analysis under a more realistic continuous-time model where the block propagation delays are heterogeneous, arbitrary, and upper bounded by some constant. The goal is to show that every valid transaction becomes permanent in all honest miners' blockchains under a certain "typical event", which occurs with probability close to 1. To that end, we establish the blockchain growth theorem, the blockchain quality theorem, and the common prefix theorem. In lieu of exponential order result in the literature, the probabilistic guarantees for the desired properties of the bitcoin and Prism protocols take the form of explicit expressions here, which provide improved design references for public transaction ledger protocols.
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