Why root over SSH is bad
There are a lot of bots out there which try to log in to your computer over SSH.
These bots work the following way.
They execute something like
ssh root@$IP and then they try standard passwords like "root" or "password123".
They do this as long as they can, until they find the right password.
On a world wide accessible server you can see a lot of log entries in your log files. I can go up to 20 per minute or more.
When the attackers have luck (or enough time), and find a password, they would have root access and that would mean you are in trouble.
But when you disallow root to log in over SSH, the bot needs first to guess a user name and then the matching password.
So lets say the list of plausible passwords has
N entries and the list of plausible users is
M entries large. The bot has a set of
N*M entries to test, so this makes it a little bit harder for the bot compared to the root case where it is only a set of size
Some people will say that this additional
M isn't a real gain in security and I agree that it is only a small security enhancement. But I think of this more as these little padlocks which are in itself not secure, but they hinder a lot of people from easy access. This of course is only valid if your machine has no other standard user names, like tor or apache.
The better reason to not allow root is that root can do a lot more damage on the machine than a standard user can do. So, if by dumb luck they find your password, the whole system is lost while with a standard user account you only could manipulate the files of that user(which is still very bad).
In the comments it was mentioned that a normal user could have the right to use
sudo and if this user's password would be guessed the system is totally lost too.
In summary I would say that it doesn't matter which user's password an attacker gets. When they guess one password you can't trust the system anymore. An attacker could use the rights of that user to execute commands with
sudo, the attacker could also exploit a weakness in your system and gain root privileges. If an attacker had access to your system you can't trust it anymore.
The thing to remember here is that every user in your system that is allowed to log in via SSH is an additional weakness.
By disabling root you remove one obvious weakness.
Why passwords over SSH are bad
The reason to disable passwords is really simple.
- Users choose bad passwords!
The whole idea of trying passwords only works when the passwords are guessable.
So when a user has the password "pw123" your system becomes insecure.
Another problem with passwords chosen by people is that their passwords are never truly random because that would then be hard to remember.
Also it is the case that users tend to reuse their passwords, using it to log into Facebook or their Gmail accounts and for your server.
So when a hacker gets this user's Facebook account password he could get into your server. The user could easily lose it through phishing or the Facebook server might get hacked.
But when you use a certificate to log in, the user doesn't choose his password.
The certificate is based on a random string which is very long from 1024 Bits up to 4096 Bits (~ 128 - 512 character password).
Additionally this certificate is only there to log into your server and isn't used with any outside services.
Monitoring root access
The comment from @Philip Couling which should have been an answer:
There's an administrative reason for disabling root. On commercial servers you always want to control access by person. root is never a person. Even if you allow some users to have root access, you should force them to login via their own user and then su - or sudo -i so that their actual login can be recorded. This makes revoking all access to an individual much simpler so that even if they have the root password they can't do anything with it. – Philip Couling
I would also add that it allows the team to enforce the principle of least privilege, with a proper sudo configuration (but writing one sounds easier then it is). This enables the team to distribute uncritical better, without giving away the key to the castle.
This article comes from the comments and I wanted to give it a bit more prominent position, since it goes a little bit deeper into the matter of botnets that try to log in via SSH, how they do it, how the log files look like and what one can do to stop them. It's been written by Peter Hansteen.
sudo -iso that their actual login can be recorded. This makes revoking all access to an individual much simpler so that even if they have the root password they can't do anything with it.