We have heard many times that bitcoins are not actually yours if private keys unlocking corresponding UTXOs are not in your possession. "Not your keys, not your coins." This postulate, this idea has became a law for people who value their financial sovereignty. Moreover, it is completely logical idea when it comes to bitcoin network itself and how things occur within the blockchain. In order for a transaction to be broadcasted it first needs to be signed with a private key and if you don't have such key, you can't spend those coins. They are not yours, they are just sitting somewhere inside blockchain.
Recently,
California court made "Not your keys, not your bitcoins" a law thus made it so not only for bitcoiners, but also for people who used to rely on third parties to store "their" coins.
This news, despite its importance for bitcoin community, is not why this topic was created. What I am really interested in is a simple question which is does this law "Not your keys" work in an opposite direction?
"Your keys, your bitcoins" sounds logical too. But there is a small problem. It is relatively easy to prove that private key is not yours if you can't spend corresponding UTXO, you can't sign a message or in case it is stored inside exchange's wallet. But how can we prove the ownership of the private key?
Like I said, we can sign a message with private key and that is considered enough, no other evidence needed. But what if someone generated the exact private key or, more realistically, have stolen it, how would it possible to prove that victim is the real possesor of private key? What would California court say in this case? If they both can sign a message, do they both have a right to these coins? Are there any other methods to prove the ownership besides signing a message?
Because if it is not possible to prove the ownership of bitcoin private key in case several people besides actual owner know private key, then "Not your keys, not your bitcoins" doesn't make sense either. It is stupid to claim that, if there is no possible way to prove that keys were ever in possesion.