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This paper proposes a novel method for secure image encryption and authentication based upon fuzzy extractor driven Elliptic Curve key exchange scheme. Use of fuzzy extractor facilitates both parties to authenticate each other without disclosing their original biometric information. The image encryption is achieved using a shared key in two steps. In the first step, we use a novel Cosine Transform based Chaos System to generate a pseudo- random chaos sequence over a dynamic range. In the second step, this chaos sequence along with Elliptic curve-based encryption is used in code block cipher mode to get the cipher image. To authenticate the encrypted image, an easily computable and verifiable digital signature scheme based on fuzzy extractor and Elliptic curve cryptography has been proposed. The proposed encryption is computationally efficient as it does not need an exclusive encoding of plain image pixels to Elliptic curve points. Results and analysis show that our scheme is resilient to different kinds of security attacks particularly differential attacks. The proposed scheme results in a random cipher image with high entropy and very low inter-pixel correlation at a low computational cost and encryption time.