Sites that are "blocked by authority" as you put it, are actually having issues with an invalid SSL Certificate from the issuing Certificate Authority.
This is not an issue with the browser, but with the website.
The certificate is purchased by a website for a certain period of time, and has to be renewed regularly.
If you have your phone configured to not automatically update the date and time, and if the date and time or incorrect, that can also cause issues with getting this message.