We consider a cognitive radio (CR) network consisting of a secondary transmitter (ST), a secondary destination (SD) and multiple secondary relays (SRs) in the presence of an eavesdropper. We rely on careful relay selection for protecting the ST-SD transmission against the eavesdropper with the aid of both single-relay and multi-relay selection. To be specific, only the "best" SR is chosen in the single-relay selection for assisting the secondary transmission, whereas the multi-relay selection invokes multiple SRs for simultaneously forwarding the ST's transmission to the SD. We analyze both the intercept probability and outage probability of the proposed single-relay and multi-relay selection schemes for the secondary transmission relying on realistic spectrum sensing. We also evaluate the performance of classic direct transmission and artificial noise based methods for the purpose of comparison with the proposed relay selection schemes. It is shown that as the intercept probability requirement is relaxed, the outage performance of the direct transmission, the artificial noise based and the relay selection schemes improves, and vice versa. This implies a trade-off between the security and reliability of the secondary transmission in the presence of eavesdropping attacks, which is referred to as the security-reliability trade-off (SRT). Furthermore, we demonstrate that the SRTs of the single-relay and multi-relay selection schemes are generally better than that of classic direct transmission. Moreover, as the number of SRs increases, the SRTs of the proposed single-relay and multi-relay selection approaches significantly improve. Finally, our numerical results show that as expected, the multi-relay selection scheme achieves a better SRT performance than the single-relay selection.