[plopilop]

Are you sure about (b) and (c)? They seem quite wrong to me. Just looking at the abstract of [0], one can have homomorphic equality test in a semi-honest model, which already seems good enough. The abstract does not point any theoretical limit either.

(a) is a classical side-channel attack, and as I say non-homomorphic libraries already take these kinds of attacks in consideration. HE won't be an exception to that, depending on what level of privacy is needed.

I did not understand what you mean by (d), and to be honest by (b) either. If you have any papers/blogs about that I'll be glad to read them.

And yes I agree, successful FHE system is inexistent as for now. But the evidence of the bare existence of FHE is only ten years old, somewhat practical FHE is even younger. We've not even reached practical FHE yet, security issues will be tackled when they will become the blocking point. At this point of the technology you can't expect research to be immediately applicable. ZK proofs were first designed in the 80s, and as far as I know they only started to be used in practice (zk-SNARKS for instance) recently.

[0]: https://ieeexplore.ieee.org/document/7941933/