"POSSIBLE BREAK-IN ATTEMPT!" in /var/log/secure — what does this mean?

Solution 1:

Unfortunately this in now a very common occurrence. It is an automated attack on SSH which is using 'common' usernames to try and break into your system. The message means exactly what it says, it does not mean that you have been hacked, just that someone tried.

Solution 2:

The "POSSIBLE BREAK-IN ATTEMPT" part specifically, is related to the "reverse mapping checking getaddrinfo failed" part. It means the person who was connecting didn't have forward and reverse DNS configured correctly. This is quite common, especially for ISP connections, which is where the "attack" was probably coming from.

Unrelated the the "POSSIBLE BREAK-IN ATTEMPT" message, the person is actually trying to break in using common user names and passwords. Do not use simple passwords for SSH; in fact the best idea to to disable passwords altogether and use SSH keys only.