Abstract
In blockchains using the Proof-of-Work (PoW) consensus mechanism, a mining pool is a joint group of miners who combine their computational resources and share the generated revenue. Similarly, when the Proof-of-Stake (PoS) consensus mechanism is adopted, the staking pool imitates the design of the mining pool by aggregating the stakes. However, in PoW blockchains, the pooling approach has been criticized to be vulnerable to the block withholding (BWH) attack. BWH attackers may steal the dividends from victims by pretending to work but making invalid contributions to the victim pools. It is well known that BWH attackers against PoW face the miner's dilemma. To our knowledge, despite the popularity of PoS, we are the first to study the pool BWH attack against PoS. Interestingly, we find that, for a network only consisting of one attacker pool and one victim pool, the attacker will eventually manipulate the network while the victim will vanish by losing the stake ratio gradually. Moreover, in a more realistic scenario with multiple BWH attacker pools and one solo staker who does not join any pools, we show that only one lucky attacker and the solo staker will survive, whereas all the other pools will vanish gradually, revealing the staker's dilemma. These findings indicate that, compared to PoW, the BWH attack on PoS has a much more severe impact due to the attacker's resource aggregation advantage. Our analysis is supported by experiments on massive real blockchain systems and numerical simulations.