Abstract: This paper describes the problem of building secure
computational services for encrypted information in the Cloud
Computing without decrypting the encrypted data; therefore, it meets
the yearning of computational encryption algorithmic aspiration
model that could enhance the security of big data for privacy,
confidentiality, availability of the users. The cryptographic model
applied for the computational process of the encrypted data is the
Fully Homomorphic Encryption Scheme. We contribute a theoretical
presentations in a high-level computational processes that are based
on number theory and algebra that can easily be integrated and
leveraged in the Cloud computing with detail theoretic mathematical
concepts to the fully homomorphic encryption models. This
contribution enhances the full implementation of big data analytics
based cryptographic security algorithm.