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In the recent times, the use of cloud computing has gained popularity all over the world. There are lots of benefits associated with the use of this modern technology, however, there is a concern about the security of information during computation. A homomorphic encryption scheme provides a mechanism whereby arithmetic operation on the ciphertexts produces the same result as the arithmetic operation on plaintexts. Concept of homomorphic encryption (HME) is discussed with reviews, applications and future challenges to this promising field of research