Login to wordpress from another PHP site

This is quite difficult for me. Help me out.
I’ve a website created with cake PHP in root domain (say mysite.com) and a blog in a directory called “blog” (mysite.com/blog).
I have a register/login feature in the PHP site. So what I want here is, whenever a member login to the main site using the PHP login form, and after he open the blog (mysite.com/blog), he should logged-in as the same user logged in the main PHP site. In the same way, whenever a new user sign-up with the registration form in the main PHP site, he should become an user in the wordpress blog.
please help me in the case of login only.
Thanks in Advance.