  It has been a long standing problem to securely outsource computation tasks
to an untrusted party with integrity and confidentiality guarantees. While
fully homomorphic encryption (FHE) is a promising technique that allows
computations performed on the encrypted data, it suffers from a significant
slow down to the computation. In this paper we propose a hybrid solution that
uses the latest hardware Trusted Execution Environments (TEEs) to assist FHE by
moving the bootstrapping step, which is one of the major obstacles in designing
practical FHE schemes, to a secured SGX enclave. TEEFHE, the hybrid system we
designed, makes it possible for homomorphic computations to be performed on
smaller ciphertext and secret key, providing better performance and lower
memory consumption. We make an effort to mitigate side channel leakages within
SGX by making the memory access patterns totally independent from the secret
information. The evaluation shows that TEEFHE effectively improves the software
only FHE schemes in terms of both time and space.
