Is it possible take a piece of data in secret? I want something like this, but in a digital sense:


  You and others walk into a room. Everyone knows who each of you are and everyone is doing their best to figure out what piece of paper each person is taking. Fortunately the all the paper is in a box. You bring your own envelope, shuffle the papers blindly and put one in your envelope, then walk out.


Since no one can see the inside of your envelope you're fine. The problem is the box.

If a website generates a thousand GUIDs and has to give you one of them, but isn't allowed to know who you are, how would it be done? The website must know you are eligible for a GUID, but how does it give you something to prove you may have a GUID and not know which you take?

I know you can sign something blindly, but can you take something blindly?
As Ricky Demer points out, you can take something blindly. It is called oblivious transfer. There are ways to add access control. See this paper as an example.