Say that someone knows half a private key and the corresponding public address.
Can he find out the other half of the private key somehow?
... apart from brute forcing for a billion years
Can he find out the other half of the private key somehow?
... apart from brute forcing for a billion years
You would likely be safe.
There are certain sophisticated attacks that could be done to further narrow down the possibility of what the possibility the rest of your private key is.
To keep it simple, you will likely not have your coins stolen within seconds of someone finding your private key, but it would be advisable to cease using the subject BTC address right away and to move your coins at your earliest connivence.
Note: the corresponding public address does not matter, the attacker knowing this does not make a difference (besides the fact that an attacker may know that the address they are trying to "hack" contains x amount of bitcoin
