This paper focusses on the use of homomorphic encryption schemes in solving data security in cloud computation. We started by acknowledging Gentry’s contribution on partial homomorphic encryption schemes where he constructed a somewhat homomorphic encryption based on ideal lattices using both additive and multiplicative Homomorphisms. We also noted improvement made on his construction by Dijkwherehe used integers instead of ideal lattices. Again we appreciated efforts by Braskerski based on learning with Errors (LWE) and Ring Learning with Errors (Ring LWE) problems. Besides all these efforts, the schemes still had strain on the computing storage and processing resources. We discovered that there is need to constructan encryption scheme which lessens the computational strain on the computing assets. Here, we found remedy in the use of both addition and composition operations to implement a fully homomorphic encryption scheme. A mathematical theory was translated into an algorithm implementable JAVA. We testediton a single hardware with minimum specifications: 1.5GHz, 4GB RAM and Windows 10 OS. The results showed that the new scheme supports faster encryption process, larger ciphertext sizes and is versatile. This new addition composition fully homomorphic scheme enhances data security in cloud computation thus boosts consumer confidence in the cloud services and applications.