> If you send your server two encryped numbers and ask to multiply them for you, the server may send you their addition instead, or just encrypt some constant it chooses and send you that. And you can't check that your data was processed the way you want.

I don't see how authenticated encryption would address that. In fact, I don't see how any kind of encryption can address that. Every way I can see to verify that the server is actually carrying out the correct operation would work without encryption.

Authentication proves that you are talking to the right server and that the result you got back from the server was the result it tried to send you, but whether or not that was what it was supposed to send you is out of scope for encryption.