Generating a private key for a given public key is computationally infeasible with current approaches: right now you'd just have to brute force it. But if some

Generating a private key for a given public key is computationally infeasible with current approaches: right now you'd just have to brute force it. But if someone finds a vulnerability they might be able to cut that time down to where it's commercially viable to get the private keys. At which point there's no way for anyone to prove they're the true owner of an address.