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.
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.