We study selfish mining in Ethereum. The problem is combinatorially more complex than in Bitcoin because of major differences in the reward system and a different difficulty adjustment formula. Equivalent strategies in Bitcoin do have different profitabilities in Ethereum. The attacker can either broadcast his fork one block by one, or keep them secret as long as possible and publish them all at once at the end of an attack cycle. The first strategy is damaging for substantial hashrates, and we show that the second strategy is even worse. This confirms what we already proved for Bitcoin: Selfish mining is most of all an attack on the difficulty adjustment formula. We show that the current reward for signaling uncle blocks is a weak incentive for the attacker to signal blocks. We compute the profitabilities of different strategies and find out that for a large parameter space values, strategies that do not signal blocks are the best ones. We compute closed-form formulas for the apparent hashrates for these strategies and compare them. We use a direct combinatorics analysis with Dyck words to find these closed-form formulas.
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