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In cloud computing, the combinations of various computing units are globally separated, however, electronically connected. In recent years, the number of cloud users has adequately increased in the modern societies. In order to restrict the illegal access of the intruders, a strong user authentication is required for cloud computing environment. In this regard, in this paper, we came up with a computationally productive and safer anonymous authentication pattern for cloud users. Moreover, in our scheme, mutual authentication is performed in an anonymous way between the cloud user and the cloud server to strongly verify the legitimacy of each user before providing an access into the cloud. After the successful anonymous mutual authentication, the targeted cloud service provider and the cloud users make mutual communication between them. In case of any misbehaviouring after successful mutual authentication …