The privacy and security of data is always a major concern in the current era of big data and cloud computing. Storing the data in encrypted form was the approach followed to overcome this problem. Homomorphic Encryption evolved as a technique to perform operations on encrypted data, providing the same results on working on raw data. It eliminates the access of decrypted data by third party (cloud service providers) for performing computation. Since its inception in 1978, there occurred many contributions and enhancements in this area. The main breakthrough was Fully Homomorphic encryption scheme proposed by Craig Gentry in 2009. This paper discuss about the classification of homomorphic Encryption Schemes as PHE,SWHE ,FHE and the additive and multiplicative operations and about various schemes that have been proposed from time to time in view of decreasing the computational cost involved and to widen the range of applications/domains which implements HE. Various practical implementations of Homomorphic encryption scheme are also discussed.

Keywords : Homomorphic Encryption, Cloud Storage, Privacy, Security