Abstract: The benefits of cloud storage which are cost efficiency, resilience, scalability and data high reliability, due to that all data firms is moving to the cloud that are easy to access from anyplace, anyhow, anytime. Therefore, the need to protect data has become a necessity against denial of services, unauthorized users and access. The security and trust issues are still challenges in cloud computing field which should be solved, secure the storage databases hosted by the cloud provider, the user’s data has to be released to the cloud and thus, leaves the protection-sphere of the data owner. This study focuses on various threats which are considered challenges for cloud computing and presents cryptography as a data security solution in cloud computing. Also, this study presents a framework of a hybrid cryptography algorithm through using DES and RSA for encryption and decryption phases sequentially.