Homomorphic encryption technique does some changes manipulation to be done on the encrypted data without decrypting the encrypted data. The decryption of encrypted data is the same as if some changes done on the original data. There are some partial homomorphic encryption schemes used for some practical applications like electronic voting, ecashing, multiparty computation and secret sharing etc., but they allow only certain specific computation on encrypted text. We describe how refreshing cipher text and Squashed decryption to play role on arbitrary computation on encrypted text in the fully homomorphic crypto system. In this paper based on the strengths and weaknesses of the existing homomorphic system we are doing the comparison of it. ©2006-2015 Asian Research Publishing Network (ARPN).