Cloud computing provides innumerable benefits to its customers but failing to solve information security concerns. Cloud customers and providers need to guard against data loss and theft. Encryption of personal and enterprise data is strongly recommended. Strong encryption with key management is one of the core mechanisms that Cloud Computing systems should use to protect data, so key management is an important technology that can help secure applications and data in the cloud. In this paper, a formal analysis of a user authentication protocol for cloud computing is presented. Analysis show that the protocol is vulnerable to replay and Man-in-the middle attacks. To overcome these attacks, a modified authentication protocol for the cloud computing environment is proposed.