Quantitative Comparison of Two Chain-Selection Protocols Under Selfish Mining Attack

The longest-chain and Greedy Heaviest Observed Subtree (GHOST) protocols are the two most famous chain-selection protocols to address forking in Proof-of-Work (PoW) blockchain systems. Inclusive protocol was proposed to lower the loss of miners who produce stale blocks and increase the blockchain throughput. This paper aims to make an analytical-model-based quantitative comparison of their capabilities against selfish mining attack. Analytical models have been developed for the longest-chain protocol but less to the GHOST protocol. However, the blockchain dynamics and evolution are different when adopting different chain-selection protocols. Therefore, the corresponding analytical models and/or the formulas of calculating metrics (such as miner profitability and system throughput) may be different. To address these challenges, this paper first develops a novel Markov model and the formulas of evaluation metrics, in order to analyze a GHOST-based blockchain system under selfish mining attack. Then extensive experiments are conducted for comparison and we observe that: (i) The GHOST protocol is more resistant to selfish mining attack than the longest-chain protocol from the aspect of relative revenue of selfish miners. (ii) Inclusive protocol can promote the security (evaluated in terms of miner profitability) improvement of the system which has little total computational power or a high forking probability. Additionally, the longest-chain protocol is more sensitive to inclusive protocol than GHOST protocol. (iii) It is hard for each of the two common-used difficulty adjustment algorithms to achieve higher system throughput and security.