Not really -- security by obscurity is a re-statement of the idea that the security mechanism shouldn't need to be secret for the security to have meaning. You're allowed to have secret data, just not secret mechanism.

And relying on what looks like secret data (changing the SSH port) where the number of bits of entropy is low enough that it's plausible to try them all (16) probably still counts as security by obscurity -- it might hide you from many attackers, but it's not enough to make you secure.

Relying on data that's not actually secret, just hard to find, is just insecure.

> but it's not enough to make you secure.

That's not why you change the ssh port at all.

You change the ssh port to filter out false positives, if someone is attacking you on your weirdo ssh port, it's likely an actual attack that you need to pay attention to. You still need to do the rest of the security stuff.

Ssh ports are brute forceable, passwords have a much much larger search space.

Changed SSH port is not security measure. It's needed to keep your log files clear from random network scanning.

When your SSH port is something like 53148 and you see password brute-force activity in logs it's almost always mean that somebody intentionally scanning your server.

Just a note: if you do change it, keep it below 1024. Otherwise if ssh dies anyone on the server can create a client listening on that port and steal credentials.

That's a somewhat obsolete belief – people have been scanning arbitrary ports for many, many years and SSH daemons helpfully announce themselves to search engines:

https://www.shodan.io/report/uMZDnWfT

This is a long-running problem and one with various popular solutions: restrict the source networks which you accept traffic for, disable password authentication entirely, and add some sort of rate limiting (e.g. 2004's fail2ban) for failures. Trying to reduce log volume by obscurity is futile - you really need to address the root problem and use tools which allow you to filter and aggregate effectively.

At this point, 16 bits of entropy is more than the entropy of a lot of the passwords that I've seen.

You have 10 bits of entropy at best, unless you put it above 1024, at which point if it dies, any none privileged user on the box can sniff passwords.

Why are you using passwords for SSH?

Do you actually have untrusted users on the box?

Why would you not secure the custom port to root-only?

If you are serious, you should limit SSH access to a bastion host with no unprivileged users.

Passwords are explicitly keys and not used for any other purpose.