Liveness and Consistency of Bitcoin and Prism Blockchains: The Non-lockstep Synchronous Case

Bitcoin is a peer-to-peer payment system proposed by Nakamoto in 2008. Since then, a number of protocols based on the Nakamoto consensus have been proposed to improve the blockchain throughput while maintaining a similar level of security. In addition to bitcoin, this work also studies the Prism protocol proposed by Bagaria, Kannan, Tse, Fanti, and Viswanath in 2018. The liveness and consistency properties of the bitcoin and the Prism backbone protocols have been established by assuming either explicitly or implicitly that the blockchains have finite lifespan. While the lifespan can be arbitrarily large, it is unsatisfying for the security guarantee to be dependent on this parameter. In addition, most analyses also assume lockstep synchrony, where by the end of each round all honest miners have complete information about all blocks published until then. This paper presents a streamlined and strengthened analysis of the liveness and consistency of bitcoin and Prism protocols without the finite lifespan assumption. Also, we use the non-lockstep synchronous model which assumes the block propagation delays to be heterogeneous, arbitrary, and upper bounded by some constant. A probabilistic guarantee is also provided for a transaction to become permanent in the final ledger of all honest miners. In lieu of order optimal results, these properties take the form of explicit bounds, which provide improved design references for public transaction ledger protocols.