Checking if user is logged into Drupal from another php application using Drupal services and REST
I would recommend using OAuth2.0, check out OAuth 2.0, assuming Drupal 8, otherwise there's the OAuth 1.0 for Drupal 7 (or if you're not using SSL with D8 for some reason).

This is the same tech that Facebook and Google use when you want to let people log into your site/app using their 3rd party credentials, so it should be robust enough if I understood what you were asking.