Login using the password from protected pages

Hi

Does anyone know the logic on how to do the following:

I have a login button with a password field only on the homepage, so the user enter the password and submit. Upon submission, I was hoping if the password entered can match with the passwords of the protected pages. Once there’s a single match, the user will be redirected to that password protected page as login successful.

Do u think it’s possible..? I need some hope here, thanks!