It is well-known that RANDAO manipulation is possible in Ethereum if an adversary controls the proposers assigned to the last slots in an epoch. We provide a methodology to compute, for any fraction $\alpha$ of stake owned by an adversary, the maximum fraction $f(\alpha)$ of rounds that a strategic adversary can propose. We further implement our methodology and compute $f(\cdot)$ for all $\alpha$. For example, we conclude that an optimal strategic participant with $5\%$ of the stake can propose a $5.048\%$ fraction of rounds, $10\%$ of the stake can propose a $10.19\%$ fraction of rounds, and $20\%$ of the stake can propose a $20.68\%$ fraction of rounds.

翻译：众所周知，若攻击者控制了某个时段内最后若干时隙的区块提议者，则以太坊中的RANDAO存在被操纵的可能。本文提出一种计算方法，可针对攻击者持有的任意权益比例$\alpha$，计算出策略性攻击者能够提议的最大轮次比例$f(\alpha)$。我们进一步实现了该方法，并计算了所有$\alpha$对应的$f(\cdot)$函数值。例如，我们得出以下结论：持有$5\%$权益的最优策略参与者可提议$5.048\%$的轮次，持有$10\%$权益时可提议$10.19\%$的轮次，持有$20\%$权益时可提议$20.68\%$的轮次。