This paper investigates the problem of secure and reliable communications for cognitive radio networks. More specifically, we consider a single input multiple output cognitive model where the secondary user (SU) faces an eavesdropping attack while being subject to the normal interference constraint imposed by the primary user (PU). Thus, the SU must have a suitable power allocation policy which does not only satisfy the constraints of the PU but also the security constraints such that it obtains a reasonable performance for the SU, without exposing information to the eavesdropper. We derive four power allocation policies for different scenarios corresponding to whether or not the channel state information of the PU and the eavesdropper are available at the SU. Further, we introduce the concept secure and reliable communication probability (SRCP) as a performance metric to evaluate the considered system, as well as the efficiency of the four power allocation policies. Finally, we present numerical examples to illustrate the power allocation polices, and the impact of these policies on the SRCP of the SU.