Analysis of Difficulty Control in Bitcoin and Proof-of-Work Blockchains
This provides a foundational analysis for the controls community to understand difficulty retargeting in blockchain systems, though it is incremental as it builds on existing stochastic modeling approaches.
The paper tackles the problem of modeling block arrival times in Bitcoin and proof-of-work blockchains by developing a stochastic model that explicitly treats difficulty as a random variable dependent on previous block times, deriving an explicit marginal distribution for blocktimes.
This paper presents a stochastic model for block arrival times based on the difficulty retargeting rule used in Bitcoin, as well as other proof-of-work blockchains. Unlike some previous work, this paper explicitly models the difficulty target as a random variable which is a function of the previous block arrival times and affecting the block times in the next retargeting period. An explicit marginal distribution is derived for the time between successive blocks (the blocktime), while allowing for randomly changing difficulty. This paper also aims to serve as an introduction to Bitcoin and proof-of-work blockchains for the controls community, focusing on the difficulty retargeting procedure used in Bitcoin.