I'm not sure if this is in scope of SF, but I'd like to setup a router so that it will only allow connections when a certain certificate is available on the client machine. The question is - is it possible on any cheap router?
Also note that I'd like to be able to generate the certificate not buy from some authority provider.
Oh and this is supposed to work within LAN.
Now it is time to convert the comments to an answer:
The keyword is RADIUS (Remote Authentication Dial In User Service) and can be used for authentication in networks (LAN, WAN, WLAN, Dialin, ...)
If it is possible with a "cheap" router depends on the cheapness. Some include RADIUS others don't. If you can install a modified (open source) firmware the chances are higher.