Is it possible to generate random bits (or any bits we decide) to be imported as a private key and then deducting his public key please?
EDIT (after a downvote):
I don't understood the downvote, if someone want to exprime me his feeling... We are on crypto part, I'm asking a serious question, I believed the private key can't be random and should respect some sort of mathematical curves, and so, can't be what we want. Sorry if this question is a newbie question, but I believed to be on the good part of the StackExchange to ask it, no?
For a more long explanation, the main goal is to generate a private key based on a the user's password derivation, creating(deducing) the public key to send to the server. Then to authenticate, the server send a challenge, the client re-create the private key on the fly and sign the challenge, then the server can be sure it's the good password. In case where the server DB is leaked, it's not possible to brute-force the password. I've explained that in another question.