how to disable SSH login with password for some users?

Question

On Linux (Debian Squeeze) I would like to disable SSH login using password to some users (selected group or all users except root). But I do not want to disable login using certificate for them.

edit: thanks a lot for detailed answer! For some reason this does not work on my server:

Match User !root
PasswordAuthentication no

...but can be easily replaced by

PasswordAuthentication no
Match User root
PasswordAuthentication yes

Answer 1

Try Match in sshd_config:

Match User user1,user2,user3,user4
    PasswordAuthentication no

Or by group:

Match Group users
    PasswordAuthentication no

Or, as mentioned in the comment, by negation:

Match User !root
    PasswordAuthentication no

Answer 2

There are a few ways that you can do this - first, you could concievably run a second sshd daemon on a different port with different config - its a bit of a hack, but with some chroot work it should work just fine.

Also, you could allow password authentication, but lock the passwords for all but the one user. The users with locked passwords will still be able to authenticate with public keys.