In this study, we investigate the impact of a secondary user on the security of the primary user in a cognitive radio network. In particular, we consider a spectrum underlay network consisting of a pair of primary users, a pair of secondary users, and an eavesdropper, operating in the same spectrum. The secondary user is allowed to simultaneously access the licensed frequency bands of the primary user as long as the outage probability of the primary user is kept below a predefined threshold, while the eavesdropper illegally listens to the communication of the primary network. Given these settings, an adaptive transmit power allocation policy, a closed-form expression for the outage probability, and an analytical expression for the probability of existence of non-zero secrecy capacity are formulated. Simulations show that the existence of a secondary network can enhance the probability of non-zero secrecy capacity of the primary network by causing interference to the eavesdropper.