I've just tried loading the agent (pageant), I've added the private key to its list of keys (it asked for the pass phrase too the first time), then now connecting to the n770 it no longer says that the server refuses our keys, just asks for username (user) and password and goes on. Shoult it be how I've described it? If yes, thanks to all and Bandit

It shouldn't ask for your username and password if you have the 770's .ssh directory setup right.

You may need to delete the entry in your known_hosts file after you change keys.

I've deleted the known_hosts file, but still it works like described before: I load the agent "pageant" with a saved session named "n770" and private key stored in pageant's keys list, 770's ssh dir has only the authorized_keys file in (with public key), and when I connect it just asks for username and password (no more "server refused our key" error) and gives me access. Is it weird?

Check your public key in your authorized_keys file and make sure the key is one line.
It's a long key and will wrap but it must be one line.

It's splitted on several lines. Because of the fact btw the connection freezed sometime, I've decided to uninstall dropbear (unistalling from the Application manager and manually removing /etc/rc2/@S20dropbear and /etc/init.d/*dropbear) and give OpenSSH a try. It works even if it seems somehow slower (but maybe it's a matter of the moment), WinSCP works good too, by the way I'd like to know: where do I have to put the public key of the pair now, in order to let OpenSSH find it? Is the file name still "authorized_keys"? Can it be splitted on several lines as PuttyGen saves it? Where in the net these infos can be found in order to avoid bothering you gentle and busy people there?

This really does not look like key dropbear or openssh can accept. authorized keys format is - each key on one line in format like

Thanks, that was the problem! I was using the key which Puttygen saves by chosing to save into a file, rather than the one it displayed in the textarea field.