On Analysis of the Bitcoin and Prism Backbone Protocols

Bitcoin is a peer-to-peer payment system proposed by Nakamoto in 2008. Properties of the bitcoin backbone protocol have been investigated in some depth: the blockchain growth property quantifies the number of blocks added to the blockchain during any time intervals; the blockchain quality property ensures the honest miners always contribute at least a certain fraction of the blockchain; the common prefix property ensures if a block is deep enough, it will eventually be adopted by all honest miners with high probability. Following the spirit of decoupling various functionalities of the blockchain, the Prism protocol is proposed to dramatically improve the throughput while maintaining the same level of security. Prior analyses of the bitcoin and Prism backbone protocols assume the lifespan of blockchain is finite. This paper presents a streamlined and strengthened analysis without the finite horizon assumption. Specifically, the results include a blockchain growth property, a blockchain quality property, and a common prefix property of the bitcoin backbone protocol, as well as the liveness and persistence of the Prism backbone protocol regardless of whether the blockchains have a infinite lifespan. We also express the properties of bitcoin and Prism backbone protocols in explicit expressions rather than order optimal results, which lead to tighter bounds and practical references for public transaction ledger protocol design.