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Recently many authentication protocols using an extended chaotic map were suggested for a mobile user. Many researchers demonstrated that authentication protocol needs to provide key agreement, mutual authentication, and user anonymity between mobile user and server and resilience to many possible attacks. In this paper, we cautiously analyzed chaotic-map-based authentication scheme and proved that it is still insecure to off-line identity guessing, user and server impersonation, and on-line identity guessing attacks. To address these vulnerabilities, we proposed an improved protocol based on an extended chaotic map and a fuzzy extractor. We proved the security of the proposed protocol using a random oracle and AVISPA (Automated Validation of Internet Security Protocols and Applications) tool. Furthermore, we present an informal security analysis to make sure that the improved protocol is invulnerable to possible attacks. The proposed protocol is also computationally efficient when compared to other previous protocols

Improving an Anonymous and Provably Secure Authentication Protocol for a Mobile User