SUMMARYCloud computing is an emerging computing area that allows on-demand, scalable, flexible, and low-cost services to the users. In cloud computing, access control and security are two major problems. In this paper, a novel authentication scheme using Chebyshev chaotic maps has been presented. The proposed model satisfies many security factors, such as scalability of login, mutual authentication, freedom of password change, two-factor security, and forward security. Two-factor security is a method that requires two credentials for authentication, where the first factor may be something that users know and the second factor may be something that users have. Forward security assures the confidentiality of the user's session key, even if the private key of the server is compromised. In addition, the proposed scheme provides users with untraceability and anonymity, which means that any kind of adversary neither gets the identities of users or servers nor link several sessions with a user or server. The proposed model is secured under the computational Diffie-Hellman assumption of Chebyshev polynomials in the random oracle model. Moreover, security and performance analysis show that the proposed scheme can resist different security attacks in cloud computing environment and it is better than existing schemes.