In the modern computing environment, smart cards are being used extensively, which are intended to authenticate a user with the system or server. Owing to the constrictions of computational resources, smart card-based systems require an effective design and efficient security scheme. In this paper, a smart card authentication protocol based on the concept of elliptic curve signcryption has been proposed and developed, which provides security attributes, including confidentiality of messages, non-repudiation, the integrity of messages, mutual authentication, anonymity, availability, and forward security. Moreover, the analysis of security functionalities shows that the protocol developed and explained in this paper is secure from password guessing attacks, user and server impersonation, replay attacks, de-synchronization attacks, insider attacks, known key attacks, and man-in-the-middle attacks. The results have demonstrated that the proposed smart card security protocol reduces the computational overhead on a smart card by 33.3% and the communication cost of a smart card by 34.5%, in comparison to the existing efficient protocols. It can, thus, be inferred from the results that using elliptic curve signcryption in the authentication mechanism reduces the computational cost and communication overhead by a significant amount.