For secure communication in an open and distributed network, three-party authenticated key exchange (3PAKE) protocol establishes a secure session key between two users with the help of a trusted server to ensure transaction confidentiality and efficiency. Existing schemes fail to achieve privacy to user's identity also unable to ensure undeniability of a service request. Therefore, we propose an authenticated three-party key exchange scheme based on the elliptic curve computational diffie-hellman assumption (ECDH). The proposed scheme not only achieves anonymity, non-repudiation but also reduces the overall computational cost. The scheme is validated in automated validation of internet security protocols and applications (AVISPA) tool and is proved secure in the random oracle model. The scheme has huge applications in real life scenarios, namely, mobile-commerce; secure message transmission, and e-voting.