Most cloud users and organizations have a great interest in adoption and use cloud services like cloud storage to store their data on cloud computing environment. With the fastest growing in cloud computing technology, user data security and privacy in cloud computing technology is one of the most critical issues because data owner stores their sensitive data onto remote cloud storage and they want to use required data from cloud storage which is not controlled and managed by them. However, successful retrieval of confidential data and computation on confidential data is hard to succeed by traditional cryptographic systems. Hence, to ensure such a cloud computing security for user data stored on the cloud storage, the encryption and decryption cryptographic algorithm must support computation over encrypted data. Fully homomorphic cryptographic algorithm is one such technique that has interested homomorphic cryptographic algorithm used to secure user data in cloud server. We have developed a framework by using fully homomorphic cryptographic algorithm which based on data stored on cloud storage. The fully homomorphic cryptographic algorithm which perform computation on cipher texts (encrypted) data can be operated directly without affecting the confidentiality of the encryption algorithms. And it can more ensure confidentiality and integrity of user data and the need of cipher text retrieval it needs the cipher text retrieval technology based on cipher text retrieval method can search directly on the cipher text data to user request from remote cloud storage and it compute user request in confidential form in untrusted cloud servers. Indeed, in this study, we evaluated complexity of derived SDC FHE and made comparison with Paillier and RSA homomorphic cryptographic algorithm with encryption time, decryption time, throughput and memory usage. The derived SDC FHE performed high on four complexity evaluation metrics than Paillier and RSA homomorphic cryptographic algorithm.