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Due to their resource constraints, Internet of Things (IoT) devices require authentication mechanisms that are both secure and efficient. Elliptic curve cryptography (ECC) meets these needs by providing strong security with shorter key lengths, which significantly reduces the computational overhead required for authentication algorithms. This paper introduces a novel ECC-based IoT authentication system utilizing our previously proposed efficient mapping and reverse mapping operations on elliptic curves over prime fields. By reducing reliance on costly point multiplication, the proposed algorithm significantly improves execution time, storage requirements, and communication cost across varying security levels. The proposed authentication protocol demonstrates superior performance when benchmarked against relevant ECC-based schemes, achieving reductions of up to 35.83% in communication overhead, 62.51% in device-side storage consumption, and 71.96% in computational cost. The security robustness of the scheme is substantiated through formal analysis using the Automated Validation of Internet Security Protocols and Applications (AVISPA) tool and Burrows-Abadir-Needham (BAN) logic, complemented by a comprehensive informal analysis that confirms its resilience against various attack models, including impersonation, replay, and man-in-the-middle attacks. Empirical evaluation under simulated conditions demonstrates notable gains in efficiency and security. While these results indicate the protocol’s strong potential for scalable IoT deployments, further validation on real-world embedded platforms is required to confirm its applicability and robustness at scale.