@hellomiakoda So the private key portion you use to authenticate against the public key portion which is uploaded to the server is supposed to be the portable secured portion. Basically that would be secured on a hardware token or encrypted USB. And you'd be able to move that from machine to machine but never copying the private key to a foreign machine.
So what is your use case, I might be able to add more clarity if I understand how you're planning to use it.
EDIT: Just re reading this and I've confused myself now. So even I need to re-read how it works LOL.