Earlier quoted context omitted.
Here’s a very simple one-time-pad style construction for homeomorphic (but not fully homeomorphic) encryption. Suppose the plaintext, ciphertext, and key, are each a natural number modulo 5. The key is selected uniformly at random. The ciphertext is obtained by adding the key to the plaintext (and as a result is also uniform random). Then the ciphertext is sent to the server. The server only has the ciphertext, which…
What does that have to do with incpa? I send this server a question encrypted. It stays encrypted yet the server distinguished my ciphertext enough to produce a coherent reply. That means there was enough information in the ciphertext for the server to perform the inference, even if it was obscured to where it looks indistinguishable, it apparently wasn't. This doesn't remove trust from the equation, it puts the trus…
The price that HE is paying is essentially "have to run every possible contributing computation", which means it has to scale extremely badly for anything real world complex