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ewbrownv comments on Cryptographic Boxes for Unfriendly AI - Less Wrong
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As I understand it, homomorphic encryption allows you to write programs that perform algebraic transformations on encrypted data without decrypting it in the process. What you’re looking for is a way to execute the ecrypted data as a general-purpose program without decrypting it, a much more difficult task that doesn't seem to be mentioned in the linked material. Is there any reason to think that such a thing is possible?
Perhaps the wikipedia article was a bad link, because it talks about things from the algebraic perspective. Algebraic operations are equivalent to general-purpose programs if you are willing to let things run more slowly; it turns out that computers are built out of ANDs and ORs, which is exactly what homomorphic encryption lets you do. For C programs the slowdown is significant. For logic circuits the slowdown isn't very significant. For LISP programs the slowdown is intermediate.
Okay, but the problem is still that you're looking for a way to execute operations without knowing what the operations are.