Cloud computing is one of the latest technology trend of the IT trade for business area. Cloud computing security converged into a demanding topic in the sector of information technology and computer science research programs. Cloud Computing is a conceptual service based technology which is used by many companies widely these days. Elliptical Curve Cryptography based algorithm provides a highly secure communication, data integrity and authentication, along with the non-repudiation communication and data confidentiality. Elliptical Curve Cryptography is known as a public key encryption technique based on the Elliptical Curve theory that can be used to create speedy, tiny and more efficient cryptography key. It has three protection points: authentication, key generation and encryption of data. This paper will create cloud security and data security of cloud in cloud computing by creating digital signature and encryption with elliptical curve cryptography