Homomorphic encryption in the cloud

Since the first notions of fully homomorphic encryption more than 30 years ago, there has been numerous attempts to develop such a system. Finally, in 2009 Craig Gentry succeeded. Homomorphic encryption brings great advantages but it seems that, at least for now, it also brings many practical difficulties. Furthermore, in the last couple of years, several other fully homomorphic systems arose where each has its one advantages and drawbacks. However, with the developments in cloud computing, we need it more than ever to become practical for real-world usages. In this paper we are discussing the strengths and weaknesses of homomorphic encryption and we give a brief description of several promising fully homomorphic encryption systems. Next, we give a special attention to the homomorphic encryption systems for cloud computing. Finally, we discuss some recent developments by IBM and their open-source library for homomorphic encryption.