Membership Bridging Joomla - PHP

Hello, i'm creating a membership site with traditional php, now my front end use joomla CMS, i would like to have extension that can bridge my joomla site with my membership site. this is a bridge extension not a convert my membership site into joomla.. my plan is : 1. if log from joomla it will also automatically log to membership site (right now i use wrapper) 2. When log from joomla the default user level will be registered, i have my own user level system in my membership site.. 3. When user log in. Declare a SESSION within joomla that can be detected from membership site This is rough idea.. another idea is welcome