Unstable Throughput: When the Difficulty Algorithm Breaks

Abstract: In Proof-of-Work blockchains, difficulty algorithms serve the crucial purpose of maintaining a stable transaction throughput by dynamically adjusting the block difficulty in response to the miners' constantly changing computational power. Blockchains that may experience severe hash rate fluctuations need difficulty algorithms that quickly adapt the mining difficulty. However, without careful design, the system could be gamed by miners using coin-hopping strategies to manipulate the block difficulty for profit. Such miner behavior results in an unreliable system due to the unstable processing of transactions. We provide an empirical analysis of how Bitcoin Cash's difficulty algorithm design leads to cyclicality in block solve times as a consequence of a positive feedback loop. In response, we mathematically derive a difficulty algorithm using a negative exponential filter which prohibits the formation of positive feedback and exhibits additional desirable properties, such as history agnosticism. We compare the described algorithm to that of Bitcoin Cash in a simulated mining environment and verify that the former would eliminate the severe oscillations in transaction throughput.