Application setup similar to REST

I am setting up a system which will take requests, query a database and provide a response (in its simplest form).

The setup will be as follows.

A client. @ http://ift.tt/1MGib5T A server. @ www.example-api.com

The client will make a Ajax request to the server. The server will authenticate the origin. Query the DB and provide a response.

What methods should I look into for me to authenticate, server/api side that the request has come from http://ift.tt/1MGib5T.

I understand this is / is similar to a RESTful api. However I do not really require for the client to login. It will all valid requests will only come from http://ift.tt/1MGib5T.

In the future they may come from mobile apps ect. However this does not need to be dynamically validated.

Thank you