Ability to hide Event Description information in event pop-up window.

I’ve created a category called Private Event. I know I can restrict it’s view to only logged in users. However, I would like anyone to see an event created with this category except they can’t see the Event Description information via the pop-up window (unless they were a logged in user). For example, the Event Title would always have Private Event for every event and the Event Description would be the detail for each private event. Anyone can then see the private events in the calendar, but when they click on the event, the Event Description would not be displayed. The Event Description information would only be displayed for logged in users. Is this possible? Maybe via code in the functions.php file?