I found that I can hide the contetnts of a page from unauthenticated users by setting:
access: site.login: true
in the Advanced page properties.
But I cannot find a way to also hide the menu. When user login form is shown, unfortunately all sections and menu is still browsable, which allows for at least deducing what is written about, what techs are used, etc.
Is it possible to hide menu when user is unauthenticated and display it as usual after log in?