You should be able to solve this.

A group of jealous professors is locked up in
a room. There is nothing else in the room but pencils
and one tiny scrap of paper per person. The profes-
sors want to determine their average (mean, not me-
dian) salary so that each one can gloat or grieve over
his or her personal situation compared to their peers.
However, they are secretive people, and do not want to
give away any personal salary information to anyone
else. Can they determine the average salary in such a
way that no professor can discover any fact about the
salary of anyone but herself? For example, even facts
such as "three people earn more than $40,000" or "no
one earns more than $90,000" are not allowed.

>>10
There's a puzzle involving sending a diamond through a corrupt postal system. Any unlocked boxes sent through the mail will be opened and their contents stolen, any keys sent through the mail will be stolen as well, just for kicks. How do you send your friend this diamond?

The answer is you put a lock on a box containing the diamond, send that to your friend, he puts his own lock on, sends it back, you unlock your lock, and send the box back to him. The box now only has his lock on it, he unlocks it and now has the diamond.

Your method is trying to do the same with encryption, each professor puts his lock on, stores his diamond, and then they all remove the locks in turn. However, because the process is (apply encryption1, apply encryption2, apply decryption1, apply decryption2), the encryption is necessarily commutative. I believe that for all commutative encryptions, seeing the result before and after decryption reveals the decryption key, and ruins the encryption, so the locked box method cannot be applied to cryptography.

I might be wrong about that though. Anyone care to go more in depth?