  The goal of this chapter is to present a survey of homomorphic encryption
techniques and their applications. After a detailed discussion on the
introduction and motivation of the chapter, we present some basic concepts of
cryptography. The fundamental theories of homomorphic encryption are then
discussed with suitable examples. The chapter then provides a survey of some of
the classical homomorphic encryption schemes existing in the current
literature. Various applications and salient properties of homomorphic
encryption schemes are then discussed in detail. The chapter then introduces
the most important and recent research direction in the filed - fully
homomorphic encryption. A significant number of propositions on fully
homomorphic encryption is then discussed. Finally, the chapter concludes by
outlining some emerging research trends in this exicting field of cryptography.
