Hide ‘Protected Pages’ subpages

I’ve tried without success to protect my website. I would like that wordpress, when ‘rendering’ a requested Page, would check if a Parent Page (or one above it) is protected and if it is, not show that subpage (and show that password authentication).. If a user is authenticated (with the protected Parent’s page), the subpage displays normaly.

What I am basically describing is not very strange: If a Page is Protected, why should a subpage not be??

Until now, I managed this by password protecting EACH subpage with the same password..