I think the way forward will be the App Licensing Service offered by Google Play :

  

Google Play offers a licensing service that allows you to enforce licensing policies for apps you publish on Google Play. With Google Play Licensing, your app can check Google Play at run time to obtain licensing status for the current user, then allow or discontinue use as the case may be.

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And below we can read:

  

The licensing service is a secure means of controlling access to your applications. When an application checks the licensing status, the Google Play server signals the response status of the licensing using a key pair that is associated exclusively with the application. The application stores the public key in its compiled .apk file and uses it to check the licensing status response.

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There are a number of steps to follow, but you can check out the step-by-step guide provided:

Adding Licensing to the App