My situation is the following: I'm within my business logic (REST operation) and need the current user.
Authentication is the process of verifying the identity of a user. In ArcGIS Server, this can be done by using either ArcGIS token-based authentication or web server authentication
ArcGIS Server provides a proprietary token-based authentication mechanism where users can authenticate themselves by providing a token instead of a user name and password. An ArcGIS token is a string of encrypted information that contains the user's name, the token expiration time, and some proprietary information. To obtain a token, a user provides a valid user name and password. ArcGIS Server verifies the supplied credentials and issues a token. The user presents this token whenever accessing a secured resource.
For highest security, web-tier authentication is recommended.