Can homomorphic encryption achieve program integrity (verification) in the cloud?
Can I use homomorphic encryption to keep cloud computation confidential and also guarantee the integrity of computation?


You're looking for verifiable computing:


  Verifiable computing (or verified computation or verified computing) is enabling a computer to offload the computation of some function, to other perhaps untrusted clients, while maintaining verifiable results. The other clients evaluate the function and return the result with a proof that the computation of the function was carried out correctly.