Cognitive radio network concept has been considered as a promising solution to improve the spectrum utilization. However, it may be vulnerable to security problems as the primary user (PU) and secondary user (SU) access the same resource. In this paper, we consider a system model where an eavesdropper (EAV) illegally listens to the PU communication in the presence of a SU transmitter (SU-Tx) communicating with a SU receiver (SU-Rx). The SU-Tx transmit power is subject to the peak transmit power constraint of the SU and outage probability constraint of the PU. Given this context, the effect of the interference from the SU-Tx to the EAV on the primary system security is investigated. In particular, analytical expressions of the probability of existence of non-zero secrecy capacity and secrecy outage probability of the PU are derived. Moreover, the performance analysis of the secondary network is examined where closed-form expressions of the symbol error probability and achievable rate are presented. Numerical examples are provided to evaluate the impact of the primary system parameters and channel conditions among users on the system performance of secondary and primary networks. Interestingly, our results reveal a fact that the security of the primary network strongly depends on the channel condition of the SU-Tx to the EAV link and the transmit power policy of the SU-Tx. Copyright (C) 2015 John Wiley & Sons, Ltd.