two problems

1. Is it possible for a remote server to prove that the software it runs is what it claims to run to the client.

2. Is it possible for a piece of software to operate on encrypted content in such a way that the owner of the machine cannot know what the software is doing, and no information about the data being processed is exposed?

>>1 not super-clear, but lets see..
1. the server could send a hash of the executable... (not very foolproof as is, it could run a different program, and just send the hash of the one it should be running..)
2. freenet kind of does this (but it doesn't do much of any processing, just stores & retrieves encrypted data)