Earlier quoted context omitted.
These are good questions! FHE appears nonintuitive at first glance, but hopefully with a smaller example it can be made clear. > Wouldn't the information required to identify what a "word" is require the running software to be able to see breaks/periods/etc? Yes. But that information can be encrypted and still computed on. You might suppose that since encrypted data is essentially gibberish, then multiplying or addin…
Great explanation, thank you. In your example you decryped by key^2. The decryption requiring a different or derivative key a general feature of the algorithm or just a quirk of your example?
It's also somewhat definitional. We're taking an established encryption scheme in both cases and constructing a new algorithm on top of it. Above where I say we're performing decryption with a key set to key^2, we could also think of it as doing Dec(key, key*m) where the key is the same but we've done some operation on the cyphertext.