## 1 Introduction  
Over the past few years, due to the rapid growth of mobile devices, there has been a dramatic increase in the number of wireless services and applications. Consequently, the demand for spectrum resources has increased, and spectrum scarcity has become a more and more serious problem. To address these emerging issues, researchers have been developing new paradigms in network design. Hence, emerging wireless technologies, such as cognitive radio networks (CRNs) [1; 2], were introduced to improve the efficiency in the spatial utilization of the radio spectrum [3; 4; 5; 6; 7; 8; 9]. The basic idea of a CR network is to allow unlicensed radio users, called secondary users (SUs), to share frequencies assigned to licensed users, called the primary users (PUs). In order to avoid interfering with the operations of the licensed user, the SU is allowed to be active when the frequency is not used by the corresponding PU. However, when the presence of the PU is detected, the SU has to vacate the occupied frequency. Due to the development of data sharing among wireless communications networks and the broadcast nature of the wireless medium, the sensitivity of the data being sent through wireless networks is vulnerable to security threats. These threats are not only in hostile environments such as national defense and national security, but also in covert commercial networks handling private and sensitive information [10]. These increasing threats have caught the attention of service providers, who have recently introduced new security measures to target these problems [10]. Because of the dynamic access manner in CR communications, the issues of information safety and security require significant consideration due to many threats in the operating environments [11; 12; 13; 14]. In particular, the physical layer of CR networks is supposed to have the ability to perform spectrum sensing and learn the surrounding radio frequency (RF) environment, and then, the CR network can dynamically access a frequency band that was assigned to a PU [15; 16; 17; 18]. However, it is also a critical weakness that can be exploited by an adversary for launching attack activities [19; 20; 21; 22; 23; 24]. The most common attacker in the physical layer is an eavesdropper because of the simple process, but high efficiency. In addition, there is no doubt that eavesdroppers become more challenging when the SU must monitor various parameters, such as PUs' activity and any potential or suspected eavesdropping, before deciding on its own operations. Subsequently, the threat from eavesdroppers is becoming a major concern for CR communications. Many aspects of security in cognitive radio have been investigated [19]. However, the influence of eavesdroppers on SU secrecy rates and the spectrum sharing process has had little consideration. Previous research such as [25; 26] proposed beamforming, optimal power allocation, and artificial jamming (AJ) to protect secret communications against eavesdroppers. In [27], the authors investigated physical layer security against eavesdropping attacks in CRNs by introducing a multiuser scheduling scheme to achieve multiuser diversity while improving the security level of cognitive transmissions with a PU quality-of-service (QoS) constraint. Most researchers considered power allocation and AJ in which all SUs cooperate to defend against eavesdroppers. For efficient spectrum utilization in CR networks, many channel selection mechanisms have been extensively studied in the existing literature [28; 29; 30; 31; 32; 33]. Most of these mechanisms consider only the remaining idle duration of the channel. For instance, [PERSON] et al. [28] used the availability of the spectrum and the idle channel duration to decide whether the SU will access the primary channel or not. [PERSON] et al. [29] proposed a rank-based channel selection scheme for efficient license bands' exploitation.