Moodle module type

I am tasked with writing a relatively small and simple PHP web app which will use a small database. Authentication for this will be through randomly generated hex keys in the query string which are generated by an administration page and emailed to desired users. This is all fine so far, but here's the catch: For various political reasons, we are forced to make this app a Moodle module. I can use the Moodle database in MySQL, but I will be working with my own tables which do not interact with Moodle, and Moodle will not interact with my tables. I must also to use the Moodle database abstraction rather than direct PHP->MySQL access. I do not want my users to know they are operating within Moodle. They shouldn't need to log in to Moodle to access my web app, and they probably won't have access to Moodle anyway. Those users who do have access to Moodle shouldn't see this web app in their list of Moodle functions. I've thrown together a few small PHP pages, included some Moodle libs, and placed the code in the moodle/mods directory. Accessing the PHP pages on the server with the URLs directly result in a Moodle error, since I'm not accessing the module through proper channels. I get the "Incorrect access detected" error. Is what I'm tasked to do even possible? If so, how is the best way to accomplish it? Do I need to write an authentication module and then an activity module? Is there any way to bypass all of Moodle's authentication and simply use the database abstraction *without* editing the core Moodle configuration files? (I know it's possible by modifying the Moodle code, but that is sadly not an option). I have plenty of PHP experience, but I only have about 4 hours of Moodle experience and I'm getting nowhere fast.