The Internet of Things (IoT) is a significant branch of the ongoing advances in the Internet and mobile communications. Yet, the use of a large number of IoT devices can severely worsen the spectrum scarcity problem. The usable spectrum resources are almost entirely occupied, and thus, the increasing demands of radio access from IoT devices cannot be met. To tackle this problem, the Cognitive Internet of Things (CIoT) has been proposed. In a CIoT network, secondary users, i.e., sensors and actuators, can access the licensed spectrum bands provided by licensed primary users (such as cellular telephones). Security is a major concern in CIoT networks. However, the traditional encryption method at upper layers (such as symmetric and asymmetric ciphers) may not be suitable for CIoT networks since these networks are composed of low-profile devices. In this paper, we address the security issues in spectrum-leasing-based CIoT networks using physical layer methods. Considering that the CIoT networks are cooperative in nature, we propose to employ cooperative jamming to achieve secure transmission. In our proposed cooperative jamming scheme, a certain secondary user is employed as the helper to harvest energy transmitted by the source and then uses the harvested energy to generate an artificial noise that jams the eavesdropper without interfering with the legitimate receivers. The goal is to minimize the Signal to Interference plus Noise Ratio (SINR) at the eavesdropper subject to the Quality of Service (QoS) constraints of the primary traffic and the secondary traffic. We formulate the minimization problem into a two-stage robust optimization problem based on the worst-case Channel State Information of the Eavesdropper (ECSI). By using Semi-Definite Programming (SDP), the optimal solutions of the transmit covariance matrices can be obtained. Moreover, in order to build an incentive mechanism for the secondary users, we propose an auction framework based on the cooperative jamming scheme. The proposed auction framework jointly formulates the helper selection and the corresponding energy allocation problems under the constraint of the eavesdropper's SINR. By adopting the Vickrey auction, truthfulness and individual rationality can be achieved. Simulation results demonstrate the effective performance of the cooperative jamming scheme and the auction framework.