Mobile API Security

I am working on a mobile application that cominique with REST ws I want to give in my application the two possibility use with connection (this feature is simple with just authentication with user and password) but want to secure my APIs so that when using APIs without authentication my API only allows my app as a client

One solution i thought was to embed some kind of hardcode string so when mobile app will use the restful url they will pass that in encryption format over ssl. But i know this seems like very bad solution..

kindly suggest what should be the best solution under such situation.