Many of today's crypto currencies use blockchains as decentralized ledgers and secure them with proof of work. In case of a fork of the chain, Bitcoin's rule for achieving consensus is selecting the longest chain and discarding the other chain as stale. It has been demonstrated that this consensus rule has a weakness against selfish mining in which the selfish miner exploits the variance in block generation by partially withholding blocks. In Ethereum, however, under certain conditions stale blocks don't have to be discarded but can be referenced from the main chain as uncle blocks yielding a partial reward. This concept limits the impact of network delays on the expected revenue for miners. But the concept also reduces the risk for a selfish miner to gain no rewards from withholding a freshly minted block. This paper uses a Monte Carlo simulation to quantify the effect of uncle blocks both to the profitability of selfish mining and the blockchain's security in Ethereum (ETH). A brief outlook about a recent Ethereum Classic (ETC) improvement proposal that weighs uncle blocks during the selection of the main chain will be given.
Compared to selfish mining in Bitcoin, the concept of rewards for uncle blocks, as done in Ethereum, lowers the amount of computational power at which selfish mining becomes a viable strategy. In Bitcoin the threshold for γ = 0.5 is 0.25, the threshold in Ethereum may be as low as 0.185 depending on the honest network’s stale block ratio.
Optimized strategies possibly lower this threshold even further. Moreover, the overall network’s resilience against other attacks – such as double spending – is significantly lowered during selfish mining caused by a high stale block ratio. Any attacker would then need less mining power to outrun the overall network temporarily or even entirely. The adaption of optimal selfish mining strategies as well as the in-depth-analysis of countermeasures is left for future work.