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In his recent paper, Vitalik often mentions the term "honest nodes". What do we mean by that exactly?

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An honest node is one which behaves in the way that we expect nodes to behave. This means that the node does not try to modify history, serves blocks and transactions correctly, transmits messages correctly, transmits correctly formatted messages and data, etc. These are all things that have a correct way of doing and honest nodes are ones which do all of these correctly.

This is opposed to malicious nodes which do not behave in the way that we expect nodes to behave. Such nodes may send malformed messages, send incorrect data, send too much or too little data, etc. These are things that are the wrong version of what a node is supposed to do, thus these nodes are behaving in a way that is not what we expect nodes to behave.

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An honest node is a node that does not try to modify history. This is opposed to an attacker node which tries to modify a past block in the blockchain presumably to benefit them financially.

Note that because transactions are cryptographically signed, "An attacker can only try to change one of his own transactions to take back money he recently spent," Bitcoin Whitepaper.

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