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The question in question: Undetectable Nothing-at-Stake - why does it matter?

Undetectable Nothing-at-Stake - why does it matter?

The paper Formal Barriers to Longest-Chain Proof-of-Stake Protocols (Brown-Cohen, Narayanan, Psomas, Weinberg, 2018) describes an attack called Undetectable Nothing-at-Stake (p. 11, 4.2 - Recency, Definition 11). I don't understand why this attack matters. The paper says

Depending on reward scheme, there may be an expected monetary gain for [undetectably] announcing [blocks on different forks].

As far as I understand it, the attacker simulates multiple independent miners like in a Sybil attack. But for the attack to be undetectable, it also needs to divide its stake among the miners it simulates. This way, each of the miners has only a fraction of the stake, so it can only mine as much as an independent, honest miner with this fraction of the stake. Otherwise it could be detected. This is because it can only behave the same way an honest miner with a high latency connection might behave. How can this lead to a higher gain?

I honestly don't know if it's on topic for ethereum.se. I don't know if this paper applies to ethereum. I could certainly trick-rephrase the question in a way to make it on-topic, e.g. "Does this problem arise in Ethereum, and how is it solved here?", but that's not really the main focus of what I want to know.

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For me it's a valid question as the Proof-of-Stake distributed consensus algorithm is implemented by Ethereum 2.0.

However, this paper is very specific. Therefore, to increase the chances of receiving an answer, you should summarize the key points about it in your question.

You can also try posting on this site: https://ethresear.ch/. It's dedicated to Ethereum research, and there is a section for consensus algorithms.

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The answer by @clement is good: posting your question here can work but it would need to be described more.

Some things to add:

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