First of all you should ask yourself why you want do this. And obviously answer that too ...

Too often people feel like protecting their work using serials and stuff like that just to realize they provide little or no protection at all. Consider what happens when someone manages to replicate you serial generation process (which will eventually happen as your application is more and more used by people), or more simply one of your clients puts his/her serial on the Net. ;-)

On the other hand you could issue PGP certificates signed with your secret key, and have your application check the certificate fingerprint for authenticity. Of course that doesn't stop anyone from distributing one of your certs ... but if you really want to do this there's nothing to stop you.

Keep in mind that your app is in the user's hands, so anyone with some time and knowledge can trick it into "thinking" any other certificate is the "right" one.

You might find The Case of Quake Cheats illuminating about what that means.