Addition-Composition Fully Homomorphic Encryption is given in this paper to solve data security equation in cloud computation. An earlier attempt to solve security problem has been proposed by Craig Gentry, who combined additive and multiplicative operations, using lattice-based cryptography. Its construction started as a somewhat homomorphic encryption scheme that evaluates low-degree polynomials over encrypted data. He then modified it to make it bootstrappable and showed that any bootstrappable fully homomorphic encryption scheme can be converted into a fully homomorphic encryption. Subsequent efforts to improve on Craig’s work still favor his approach, i.e. bootstrapping homomorphic cryptosystems with noisy ciphertexts into fully homomorphic cryptosystems. The approach in the design of the scheme in this paper is based on combining additive and composition properties making it complex to compromise. Finally, the scheme enables secure computation of cloud data without exposing it to deliberate risk.