Langindpage with user login to access private galleries, but without password

Hi,

At the moment I use private galleries and the common user login interface (lock on my website in header).

What I want to do is the following:
Landing page with just a field called “Name” and a captcha (solving a formula or sth).

A user gets a link to for example demo.141080.com and there is the landing page. He enters his first name and solves the captcha and clicks “Start” or sth. After that, he sees the pages and posts that are set to private.

Question: I can create the landing page, but what plugin do I need to solve the user login thing?

The page I need help with: [log in to see the link]