When you start initializing an address in your wallet (or when you create an address by your own) what basicaly happens is that your PC will randomly(!) generate a private key (following rules, ofc.).
Out of this private key you can calclulate your public key (an address is the 'visualisation' of a public key). This is a one-way-function. This means you can generate the pub key out of the priv key easily..
I see. Seems pretty secure. The last problem that I have then is how hard would it be to imitate the public key? a public key is derived from the private one but it is considerably shorter (64-bit?). Shouldn't multiple private keys match that public key? couldn't it be possible (and easier than a brute force on the private key) to simply find something that hashes out to the private key as it is the only part that is actually verified?
Yes, “straight up brute forcing” is indeed
possible. I sincerely suggest that you try this. It will keep you busy and out of trouble. To make it easier, there is a
public directory of all Bitcoin private keys. Yes, that site really does list
all Bitcoin private keys. Get rich! Happy hunting!
(P.S., why are highly intelligent people in a “Development & Technical Discussion” forum seriously answering questions about bruteforcing secp256k1!? Doubly-hashed, undisclosed public keys are just gravy.)
I'm just learning here and as I understand this forum's main goal is to educate/demystify/discuss bitcoin. It seems that you understand but I'm just starting to.
I appreciate everyone's help by the way. I know this must seem trivial.