In the contemporary world, the security of data and privacy policies are major concerns in cloud computing. Data stored on the cloud has been claimed to be unsafe and liable to be hacked. Users have found it difficult to trust their data in the cloud. Users want to know that their data is accessible from anywhere and that an unauthorized user will not be able to access it. Another area of concern is the authentication of users over the cloud. There are a number of security concerns with Cloud Computing which include Distributed Denial of Service, Data leakage, and many more, just to mention a few. In this paper, an Elliptic Curve Cryptography (ECC) algorithm is used for the encryption and decryption of the information stored on the cloud, so that if someone gains access to the server, it would be unable to access the original information. Performance evaluation of the developed system is performed by comparing ECC with the RSA algorithm. The results show that the ECC method is more efficient than RSA when used to secure information in the cloud.