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Cryptographic Self-Selection is a common primitive underlying leader-selection for Proof-of-Stake blockchain protocols. The concept was first popularized in Algorand [Jing Chen and Silvio Micali, 2019], who also observed that the protocol might be manipulable. [Matheus V. X. Ferreira et al., 2022] provide a concrete manipulation that is strictly profitable for a staker of any size (and also prove upper bounds on the gains from manipulation). Separately, [Maryam Bahrani and S. Matthew Weinberg, 2024; Aviv Yaish et al., 2023] initiate the study of undetectable profitable manipulations of consensus protocols with a focus on the seminal Selfish Mining strategy [Eyal and Sirer, 2014] for Bitcoin’s Proof-of-Work longest-chain protocol. They design a Selfish Mining variant that, for sufficiently large miners, is strictly profitable yet also indistinguishable to an onlooker from routine latency (that is, a sufficiently large profit-maximizing miner could use their strategy to strictly profit over being honest in a way that still appears to the rest of the network as though everyone is honest but experiencing mildly higher latency. This avoids any risk of negatively impacting the value of the underlying cryptocurrency due to attack detection). We investigate the detectability of profitable manipulations of the canonical cryptographic self-selection leader selection protocol introduced in [Jing Chen and Silvio Micali, 2019] and studied in [Matheus V. X. Ferreira et al., 2022], and establish that for any player with α < (3-√5)/2 ≈ 0.38 fraction of the total stake, every strictly profitable manipulation is statistically detectable. Specifically, we consider an onlooker who sees only the random seed of each round (and does not need to see any other broadcasts by any other players). We show that the distribution of the sequence of random seeds when any player is profitably manipulating the protocol is inconsistent with any distribution that could arise by honest stakers being offline or timing out (for a natural stylized model of honest timeouts). 

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 α of stake owned by an adversary, the maximum fraction f(α) of rounds that a strategic adversary can propose. We further implement our methodology and compute f(⋅) for all α. 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. 

We consider prophet inequalities subject to feasibility constraints that are the intersection of q matroids. The best-known algorithms achieve a Θ(q)-approximation, even when restricted to instances that are the intersection of q partition matroids, and with i.i.d. Bernoulli random variables [José R. Correa et al., 2022; Moran Feldman et al., 2016; Marek Adamczyk and Michal Wlodarczyk, 2018]. The previous best-known lower bound is Θ(√q) due to a simple construction of [Robert Kleinberg and S. Matthew Weinberg, 2012] (which uses i.i.d. Bernoulli random variables, and writes the construction as the intersection of partition matroids). We establish an improved lower bound of q^{1/2+Ω(1/log log q)} by writing the construction of [Robert Kleinberg and S. Matthew Weinberg, 2012] as the intersection of asymptotically fewer partition matroids. We accomplish this via an improved upper bound on the product dimension of a graph with p^p disjoint cliques of size p, using recent techniques developed in [Noga Alon and Ryan Alweiss, 2020].