Check your log files regularly to see what types of attacks are being run against your server. /var/log/auth or /var/log/auth.log is a typical place to find attempted logins:
Jan 18 10:48:46 ns003 sshd: Illegal user rosa from ::ffff:184.108.40.206
Jan 18 10:48:49 ns003 sshd: Illegal user rosemarie from ::ffff:220.127.116.11
Jan 18 10:48:51 ns003 sshd: Illegal user ruth from ::ffff:18.104.22.168
Jan 18 10:48:54 ns003 sshd: Illegal user sabine from ::ffff:22.214.171.124
Jan 18 10:48:57 ns003 sshd: Illegal user sandra from ::ffff:126.96.36.199
Regularly upgrade your operating system to add security fixes. On Debian: apt-get upgrade
Monitor news on vulnerabilities at http://www.securityfocus.com/ and related websites.
Try installing grsecurity and/or SELinux and/or AppArmour and/or PaX.
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