The entrance of Internet of Things (IoT) technologies to healthcare industry has impacted the explosion of eHealth big data. Cloud computing is widely considered to be the promising solution to store this data because of the presence of abundant resources at a lower cost. However, the privacy and security of the IoT generated data cannot be ensured as the data is kept far from the owner's phys- ical domain. In order to resolve the underlined issues, a reassuring solution is to adopt attribute-based signcryption (ABSC) due to the desirable cryptographic properties it holds including fine-grained ac- cess control, authentication, confidentiality and data owner privacy. Nonetheless, executing expensive computation such as pairing and modular exponential operations in resource-constrained IoT device platform can be too taxing and demanding. To address the challenges stated above, we proposed in this paper, a more efficient scheme where computation power is borrowed from the cloud server to process expensive computations while leaving simple operations to local users. In order to realize this, trusted attribute authority, signcryptor and designcryptor outsources to the cloud expensive tasks for key gener- ation, signcryption and designcryption respectively. Moreover, validity and correctness of outsourced computations can be verified by employing outsourcing verification server. Security analysis, compar- isons evaluation and simulation of the proposed scheme is presented. The output demonstrates that it is efficient, secure and therefore suitable for application in resource-constrained IoT devices.