This paper proposes verifier-based computation-and communication-efficient three-party encrypted key exchange (VBCC3EKE) protocols to minimize the complexity of computational and communicational costs among all users and fit three-party communication environments. Compared with related verifier-based 3EKE protocols, the proposed VBCC3EKE protocols have enhanced computational and communicational efficiency. As a result, the proposed VBCC3EKE protocols are most suitable for use in various applications over distributed three-party network environments such as the Internet and mobile e-commerce.