  Performing smart computations in a context of cloud computing and big data is
highly appreciated today. Fully homomorphic encryption (FHE) is a smart
category of encryption schemes that allows working with the data in its
encrypted form. It permits us to preserve confidentiality of our sensible data
and to benefit from cloud computing powers. Currently, it has been demonstrated
by many existing schemes that the theory is feasible but the efficiency needs
to be dramatically improved in order to make it usable for real applications.
One subtle difficulty is how to efficiently handle the noise. This paper aims
to introduce an efficient and verifiable FHE based on a new mathematic
structure that is noise free.
