I'm currently making an open source browser extension that will send requests to my site. This can easily be done with Ajax, a request will be sent to the page action.php.
My site will use PHP, well now the question is, how can I make sure action.php receives the request from the original extension? I mean griefers could easily send false information to the server, or a fork could be used and send incorrect data. I thought of generating a token of some sort, but anyone could recreate it I guess.
How can I prevent this situation?
I have some experience with this myself. I've been building an extension with a login and eventually came to the inevitability that security in an extension is inherently difficult.
The issue is that an extension is just a bundle of JS and HTML that anyone can inspect the values of. This means that anyone determined enough to dig through your code can potentially find out how to bypass anything you have built in.
The solution I eventually came to is that, the extension itself cannot hold any long-lasting secrets. A session with a timeout is the only safe thing to store. The actual login for my extension is done via a website over HTTPS.
If you are trying to do this without any such login, your only recourse is to make it as difficult as possible to determine what needs to be sent by using an algorithm that can generate server verifiable tokens, and then only publishing minified code to the webstore.
EDIT: Reread the question and noticed that you said you are doing this open source. Without some sort of authentication on the webserver via HTTPS, there is little you can do to stop those determined to bypass your protections because they will be on display in your public repository.