Since most of our asymmetric encryption algorithms are going to be out-of-date in a couple of year due to Shor's algorithm, I was wondering about the future of FHE schemes. I have found this paper, which states:
"It is impossible to construct secure group homomorphic encryption in the quantum world, if the plain-text and cipher-text spaces form abelian groups."
And I'm asking: are there any candidates which are also quantum resistant?