I created a paper wallet on coinbase and wanted to import it to coinbase.com. It allowed me to import it by specifying private key only. I was surprised that I didn't have to specify public key as well... is it secure?
I am surely missing here something but the analogy that comes to my mind is ability to log in into someone's gmail account by providing only password and not email. I mean, if that would be possible we could specify "P@ssword" and I'm sure someones has this kind of password to their email, that would let us log in to that account.
Similarily, I could specify some random private key and hope that it's associated with some public address...
Could you please clarify why my reasoning is not correct and why importing bitcoins by specifying private key only is safe?