The place of cloud computing as an emerging technological paradigm enjoys incontestable status in the field of digital resource management. Computational effort in such cloud environment involves processing of data hosted under preferred deployment model. A computational requirement on the critical data resident in cloud environment is to adequately address security concerns for both cloud users and providers. Fully Homomorphic Encryption (FHE) has been employed to introduce computational complexity when processing data in the cloud without compromising its security. Previous implementations of fully homomorphic encryption scheme have enabled successful operations on such encrypted data without revealing its secret key. However, this scheme introduce computational defect since the encrypted data becomes very large causing heavy burden onto computing assets in question. In this paper, we appreciate this implementation weakness and address it by incorporating a new technique whereby we defined addition-composition operation such that η() = η()  η() where  is a composite function. Our approach not only tightens the security requirement on processed data but also lessen computational overheads, which make it ideal for cloud computation. Again, we are able to demonstrate superiority of our approach against previous variants of fully homomorphic encryption that has been implemented.