This is equivalent to the famous double-spend problem in designing decentralized currencies, except instead of the goal being to prevent a previous owner of a coin from being able to send it again, here the goal is to prevent the previous key controlling an account from being able to change the key. Just like creating a decentralized currency, doing account management in a decentralized way requires something like a blockchain. A blockchain can timestamp the key change messages, providing common knowledge over whether B or C came first.

One of the fundamental goals of a blockchain is resolving the “double spend” problem. In a nutshell, this means preventing someone from sending the same coin to two people. However, beyond just simple spend transactions, it applies any time two transactions want to update the same state. This could be someone trying to duplicate Bitcoin, or two people trying to buy the same CryptoKitty. For the sake of generality, we’ll call it the “double update” problem. Fundamentally it’s about ordering: when we see two things, how do we decide which is first, and what happens to the second one?