  Quantum homomorphic encryption (QHE) is an encryption method that allows
quantum computation to be performed on one party's private data with the
program provided by another party, without revealing much information about the
data nor the program to the opposite party. We propose a framework for
(interactive) QHE based on the universal circuit approach. It contains a
subprocedure of calculating a classical linear polynomial, which can be
implemented with quantum or classical methods; apart from the subprocedure, the
framework has low requirement on the quantum capabilities of the party who
provides the circuit. We illustrate the subprocedure using a quite simple
classical protocol with some privacy tradeoff. For a special case of such
protocol, we obtain a scheme similar to blind quantum computation but with the
output on a different party. Another way of implementing the subprocedure is to
use a recently studied quantum check-based protocol, which has low requirement
on the quantum capabilities of both parties. The subprocedure could also be
implemented with a classical additive homomorphic encryption scheme. We
demonstrate some key steps of the outer part of the framework in a quantum
optics experiment.
