eng International Academy of Ecology and Environmental Sciences Selforganizology 2410-0080 2026-12-1 13 3-4 142 150 4 article Rashid Ahmed 1 2 Riaz Shah 1 2 Mohsin Shah 1 2 Noor Ul Amin 1 2 Department of Telecommunication, Hazara University, Mansehra, KP, Pakistan Department of Computer Science, Hazara University, Mansehra, KP, Pakistan Vehicular Cloud Computing (VCC) combines vehicular ad hoc networking with cloud resources to support safety, traffic-management, infotainment, storage, and computation services. Because vehicles and roadside components communicate over dynamic wireless links, authentication, confidentiality, integrity, and resistance to impersonation and replay attacks are important requirements. This paper presents a secure authenticated key exchange scheme for VCC based on Schnorr signcryption and hyperelliptic curve cryptography (HECC). The scheme uses sender and receiver authentication phases and one-way hash operations to establish mutual authentication before data transfer. We evaluate the scheme using MATLAB and compares its computational cost with selected elliptic-curve and hyperelliptic-curve signcryption schemes. In the reported experiments, the proposed scheme requires 1.44 ms for signcryption and 1.92 ms for unsigncryption, giving a reported total of 3.36 ms. The paper also reports reduced key-size requirements for HECC relative to the ECC parameters used in its comparison. Security analysis in the source work addresses confidentiality, integrity, authenticity, and unforgeability. The results indicate a reduction in the reported computational overhead; however, the study is based on simulation and source-reported operation costs, so broader implementation and formal security validation are appropriate directions for future work. http://www.iaees.org/publications/journals/selforganizology/articles/2026-13(3-4)/an-optimal-secure-authenticated-key-exchange-scheme.pdf vehicular cloud computing VANET Schnorr signcryption hyper elliptic curve cryptography authentication key exchange security computational cost