Is this normal?

[Erlend Lorentzen <er-lore () online no>]

Hi

I'm not very experienced with this sort of thing so please bear with me.
The following concerns my Slackware 9.1 NAT/Firewall protecting my Home
LAN from the Internet.

Checking my logs today I was a bit surprised to find about 80 refused
connection attempts to my sshd during the last month like:
Oct  7 21:22:27 firewall sshd[9710]: refused connect from
xxx.xxx.xxx.xxx

I did reverse lookups on the IP's with dig and found that the attemts
originated from a variety of hosts from Italy, Polen, Russia, Sweden and
Pakistan to name but a few.

One particular host had tried connecting 19 times with just a few
seconds between tries (is he/she just trying different commonly used
passwords?)

Now to my questions:
Is this Normal?
Should I be concerned?
Any security tips, suggestions, thoughts? (I update regularly with
swaret (SlackwareTool), use strong random passwords, tcp wrappers)
Anyone know a good guide to hardening Slackware?
Anything else you'd like to mention?

Thanks, your help is much appreciated!

Best regards Erlend.