Recent development in wireless communications has lead to the problem of growing spectrum shortage. Cognitive radio, as a novel technology, has been proposed in recent years to solve this problem by dynamically accessing the spectrum so as to enhance the spectrum utilization. Security in cognitive radio networks has become a challenging issue because there are more chances open to attackers by cognitive radio technology, compared to those from conventional wireless networks. These weaknesses and vulnerable aspects, introduced by the nature of cognitive radio, may cause serious impact on the security and quality of service (QoS) provisioning for the entire network. Unfortunately, at present, there is no specific secure protocol designed for cognitive radio networks. Therefore, in this paper, we conduct a high-level survey to review and reflect the state-of-the-art work on the security issues in cognitive networks. We focus on analyzing the security system at the macroscopic level, where both protection and detection are considered to be the most essential parts to ensure security in the whole network. Furthermore, we investigate special characteristics of cognitive networks at different protocol layers, including physical layer, link layer, network layer, transport layer and application layer. We recognize both the challenges and experiences, and focus on constructing the secured cognitive wireless networks.