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GSM is one of the most dominating networks for wireless mobile communication. With the passage of time, financial institutions have started using this network for providing their services. Beginning from basic services like balance enquiry, the trend is increasing to provide financial transactions on mobile. This trend establishes the need of strengthening user authentication and requirement of network authentication as well. In this paper, we have proposed a mutual authentication approach using asymmetric cryptography. In the proposed technique, user and network are authenticated with minimal computation and signaling overhead.