Interesting! Are there any security concerns with SHE? If not, it sounds like all of the benefits of FHE with none of the downsides, other than the noise overwhelming the system. If that’s true, and SHE can run at least somewhat inexpensively, then this could be big. I was once super hyped about FHE till I realized it couldn’t be practical, and this has my old excitement stirring again.
Most FHE schemes are constructed out of SHE schemes. Also, there’s nothing preventing FHE from being practical, it’s just that existing constructions are not as fast we would like them to be
My impression is that SHE are still relatively expensive, not as crazy as FHE but still slow enough to preclude many usecases and the noise breakdown can happen relatively quickly making them not work for most algorithms people want to use FHE for.
