I answered a similar question regarding Joomla RESTful APIs here:
REST API for Joomla 3.0
Basically, I ended up developing a solution which meshes the Slim PHP micro-framework with the Joomla Framework / CMS (requires Joomla 3.4.3+).
Why?
Well, the main reason is that while using the Slim framework would be OK as a one-off solution, I realized that one would still need to develop all the accompanying ACL and access security, not to mention the actual CMS that might store and manage all the important data in the first place.
Basically, I did the work so you don't have to. Yes, it's a commercial component (must pay to download) but I think it's WELL worth it for what you end up getting out of it.
It's brand new, so the service routes in the cAPI ("Constant API") Core package are still limited, but those are being built-out over time (all included in the core package of course). The component/plugin/library package is architected to allow for easy integration of add-on plugins which will introduce new service routes to add functionality like RESTful JSON APIs for MySQL, MSSQL, MongoDB, LDAP, etc. I already use an alpha version of the LDAP add-on in a an enterprise environment, so I expect that to be available for purchase/download soon.
The point of all this is that you can use an existing Joomla site to drive mobile apps (with some development for Mosets), while taking advantage of built-in user management and ACL, along with token auth (via cAPI).
Let me know if you have any questions.