Am I required to hand out private encryption key to head of institute?
This seems like an X-Y problem. Why is important work data only kept on a computer on your desk, in the first place? I would expect it to be on a Git repository, or on the shared storage space of a workplace server. 

Once you fix this problem, the issue you mention becomes irrelevant: your data will not be lost if your disk suddenly becomes inaccessible.

So a practical way to address the issue could be offering to put more of your work data in shared servers and git repositories, so that the problem disappears. Ask your superiors which data they are worried about, and offer to keep them online preemptively.