Three-party encrypted key exchange (3PEKE) enables two communicating parties to securely exchange confidential and authenticated information over an insecure network via a trusted server. This investigation presents a novel efficient and secure 3PEKE protocol using a super-poly-to-one trapdoor function. The proposed protocol employs the Diffie–Hellman key exchange and adopts the technique that the clients can publicly exchange the factors for generating the session key without the help of the server to reduce the numbers of transmissions. A round-efficient version of the proposed 3PEKE protocol is also described. Compared with related approaches, the proposed protocol not only retains security requirements and possesses lower computational cost but also has fewer transmissions and realizes the lower bounds of communications. Copyright © 2013 John Wiley & Sons, Ltd.