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The parity implementation of Ethereum provides proof of authority as an alternative consensus mechanism.

I have not found much commentary about the advantages/limitations of this model for permissioned blockchains. For example let's imagine that there is a consortium of banks which want to interact with each other through a permissioned ethereum blockchain. Each bank owns one authoritative node which can sign blocks, and all the banks sign blocks in a round robin fashion.

What kind of attacks could one of the authorities do at the expense of the others?

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There are different algorithms for Proof of Authority. For instance Parity's Authority Round is essentially round robin, where as Rinkeby's version is more complicated. Proof of Authority is not well defined enough to list specific attacks, pick an implementation.

I think an important thing to keep in mind with Proof of Authority is that since the parties are predetermined and trusted, they probably already know each other. In your example with banks, the banks all are well established and know how to get in touch with each other. This is very different from a public network like Bitcoin or Ethereum, where actors are pseudonymous and can just make new identities on a whim.

In a PoA chain where the authorities all have established identities, it is very possible that penalties could exist outside the blockchain system. In your example with banks, legal contracts could be established between banks to ensure that detectable attacks or collusion between banks is punishable.

It's weird to think that a blockchain would fall back to legal rules, but it's also weird to think of a blockchain that is controlled by a central set of authorities.

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There are a few very detailed attacks explained in this Github EIP 225

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