[asrp]

Can you tell us what do you mean by "encrypted program"?

Do you mean that if all operations of a universal Turing machine were homomorphic then you can encryt the code with a hard-coded input and get an encrypted output?

Can you also elaborate on your server example? I don't understand what you are trying to do. (Whats an "encrypted server"?

[ajb]

Pretty much. Like mmastrac's comment (currently top). I hadn't realised people had got so far.

What you'd like to be able to do, is something like encrypt the code of a tor node in such a way that it could be run by an untrusted hosting provider, without breaking the security of tor.

[matthewdgreen]

FHE does in principle allow you to do this, but it has the limitation that the outputs of the "Tor node" will themselves be encrypted. That's ok if you have the decryption key and are the one interacting with the Tor node. It's not ok if you want the Tor node to output useful data like network packet headers that anyone can parse.

There is another field called cryptographic program obfuscation that tries to avoid this problem, and actually create "encrypted" programs that can output useful unencrypted outputs that anyone can use. There are a lot of restrictions on that type of program. Here's another long (and very high level) blog post on that: https://blog.cryptographyengineering.com/2014/02/21/cryptogr...