Are there any known PHE or FHE schemes that can run a full blown virtual machine ?
I always thought FHE was only good if you can fully unroll your "fixed-length" computation, and even then you can only use each "program" once without compromising security.
In particular the "Extractable Witness Encryption" conjecture is impossible under a reasonable falsifiable assumption: https://pdfs.semanticscholar.org/8587/dba4ff31e8118e9bd5914a...
Under that assumption, general purpose differing-inputs obfuscation cannot exist.
The way I understand it, FHE being applicable to anything other than "unwrapping a path through a circuit" seems implausible. Any claims of arbitrary encrypted computation should be viewed with the highest dose of skepticism.
Every time you want to run a computation on your FHE-enabled VPS you would need to upload data proportional to the maximum number of operations in the computation. Otherwise, re-running the same computation with a different input gives away information about both of your inputs and about the computation.
Do they actually do better than "factor the RSA key, then compute the output, then re-encrypt"?