The simplest thing you can do to protect yourself from port scan attacks or reconnaissance attacks is to use a good firewall and intrusion prevention system (IPS). It's not possible to protect against all such attacks -- after all, if you're running a Web server, port 80 is obviously going to be visible to the world -- but, this approach will limit an organization's exposure.
The firewall strictly controls which ports are exposed and to whom they are visible, limiting the attack surface discoverable with a port scan. The IPS will detect port scans in progress and shut them down before they are able to gain a full map of your network.
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This was first published in August 2009