In this paper we report on our work to design, implement and evaluate a Fully Homomorphic Encryption (FHE) scheme. Our FHE scheme is an NTRU-like cryptosystem, with additional support for efficient key switching and modulus reduction operations to reduce the frequency of bootstrapping operations. Ciphertexts in our scheme are represented as matrices of 64-bit integers. The basis of our design is a layered software services stack to provide high-level FHE operations supported by lower-level lattice-based primitive implementations running on a computing substrate. We implement and evaluate our FHE scheme to run on a commodity CPU-based computing environment. We implemented our FHE scheme to run in a compiled C environment and use parallelism to take advantage of multi-core processors. We provide experimental results which show that our FHE implementation provides at least an order of magnitude improvement in runtime as compared to recent publicly known evaluation results of other FHE software implementations.