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paulfchristiano comments on Cryptographic Boxes for Unfriendly AI - Less Wrong
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Does the uFAI have access to it's own public key? If so, I think it can produce coherent output.
All it has to do is encrypt random things with the public key, until it finds something that produces coherent-looking ciphertext from it's own perspective, and then there's a two-way channel.
Homomorphic encryption has to be randomized. If you keep the randomness secret (as the security proof of homomorphic encryption requires) then the AI can't possibly predict what the actual encryptions will look like because it doesn't know anything about the randomness used to produce them.
This can be accomplished either by generating fresh quantum randomness for each encryption, or by using a psuedorandom generator which isn't vulnerable to any passive side channel attack (certainly using fresh randomness is much safer).