I don't have a lot of experience with API's, but I do know that if you want to secure them properly, you can use some API secret keys to handle the job
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API Keys
If you want to provide functionality to only a particular group of users, you'll be best embedding API keys into their applications.
I don't know how you'd achieve this specifically (IE only for your android systems), but what you'll want to in an ideal world, is only allow particular API-key enabled accounts to access the Rails app data.
Your job will then be to provide the keys to android-powered devices only (the part I'm not sure about yet).
Rails is actually very versatile when it comes to securing an API:

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Android ID
I don't know specifically, if you're installing apps on Android devices, surely you'll get access to an Android ID or something?
Upon reading this documentation, it seems you get access to a collection of appliance ID's inside Android (both for your device and Android installation). I would be looking at how to use these as a way to identify API requests
Is there a unique Android device ID?
Perhaps your flow could be something like - the first run of the app would verify the device is Android, and if so, adds the Device ID to your rails "API Keys" db. This will then allow you to permit access to the device in the future