With the materialization of the internet of things (IoT), big data analytic and cloud computing services give rise to extra breadth in the assessment of more secure computing environments, better resource management and vulnerability analysis. In order to accurately assess the vulnerability of Bluetooth low energy (BLE) wireless network enabled IoT systems, we have proposed a novel approach to extend the calculation formula for Authentication which is one of variables used in the conventional base score equations of the Common Vulnerability Scoring System (CVSS) v2 proposed by the National Infrastructure Advisory Council. Through an example BLE wireless network based shopping cart IoT system we have demonstrated the weakness of the current CVSS v2 base score equations and how to overcome the weakness through our extension.