Lattice-based cryptography is being used for several primitives and applications.
I know there are newer works for PIR, PSI, ORAM that have seen tremendous improvements due to FHE. In some cases, FHE is the only tool that can be used for practical constructions of these primitives.
My question is which other such primitives have seen improvements (in performance or security)?
What FHE brings to secure computation (protocols such as PIR and PSI are simply special cases of secure computation) are smaller communication and allowing single-server constructions. So any kind of secure-computation will see an improvement when switching to FHE (of course, the tradeoff is more computation).
Other examples include secure machine learning, both the learning part and the prediction part, preprocessing in MPC (generating Beaver triples), secure voting and many more.
By the way, ORAM doesn't typically use FHE since more efficient constructions exists using mostly symmetric primitives.
