A cognitive radio is an intelligent wireless communication system that improves spectrum utilisation by allowing secondary users to use the idle radio spectrum from primary licensed networks or to share the spectrum with primary users. Due to several significant challenges for cryptographic approaches of upper layers in protocol stacks | for example, private key management complexity and key transmission security issues | physical layer (PHY) security has drawn significant attention as an alternative for cryptographic approaches at the upper layers of the protocol stack. Security threats may arise from passive eavesdropping node(s), which try to intercept communications between authenticated nodes. Most recent studies consider information theoretic secrecy to be a promising approach. The idea of information theoretic secrecy lies in exploiting the randomness of communication channels to ensure the secrecy of the transmitted messages. Due to the constraints imposed on cognitive radio networks by secondary networks, allocating their resources in an optimal way is a key to maximising their achievable secrecy rates. Therefore, in this thesis, optimal resource allocation and secrecy rate maximisation of cognitive radio networks (CRNs) are proposed. Cooperative jamming is proposed to enhance the primary secrecy rate, and a new chaos-based cost function is introduced in order to design a power control algorithm and analyse the dynamic spectrum-sharing issue in the uplink of cellular CRNs. For secondary users as the game players in underlay scenarios, utility/cost functions are defined, taking into account the interference from and interference tolerance of the primary users. The existence of the Nash equilibrium is proved in this power control game, which leads to significantly lower power consumption and a relatively fast convergence rate when compared to existing game algorithms. The simulation results indicate that the primary secrecy rate is significantly improved by cooperative jamming, and the proposed power control algorithm achieves low power consumption. In addition, an integrated scheme with chaotic scrambling (CS), chaotic artificial noise, and a chaotic shift keying (CSK) scheme are proposed in an orthogonal frequency division multiplexing (OFDM)-based CR system to enhance its physical layer security. By employing the chaos-based third-order Chebyshev map to achieve the optimum bit error rate (BER) performance of CSK modulation, the proposed three-layer integrated scheme outperforms the traditional OFDM system in an overlay scenario with a Rayleigh fading channel. Importantly, under three layers of encryption that are based on chaotic scrambling, chaotic artificial noise, and CSK modulation, a large key size can be generated to resist brute-force attacks and eavesdropping, leading to a significantly improved security rate. Furthermore, a game theory-based cooperation scheme is investigated to enhance physical layer (PHY) security in both the primary and secondary transmissions of a cognitive radio network (CRN). In CRNs, the primary network may decide to lease its own spectrum for a fraction of time to the secondary nodes in exchange for appropriate remuneration. The secondary transmitter (ST) is considered to be a trusted relay for primary transmission in the presence of the ED. The ST forwards a message from the primary transmitter (PT) in a decode-and-forward (DF) fashion and, at the same time, allows part of its available power to be used to transmit an artificial noise (i.e., jamming signal) to enhance secrecy rates. In order to allocate power between the message and jamming signals, the optimisation problem is formulated and solved for maximising the primary secrecy rate (PSR) and secondary secrecy rate (SSR) with malicious attempts from a single eavesdropper or multiple eavesdroppers. Cooperation between the primary and secondary transmitters is also analysed from a game-theoretic perspective, and their interaction modelled as a Stackelberg game. This study proves theoretically and computes the Stackelberg equilibrium. Numerical examples are provided to illustrate the impact of the Stackelberg game-based optimisation on the achievable PSR and SSR. The numerical results indicate that spectrum leasing, based on trading secondary access for cooperation by means of relay and a jammer, is a promising framework for enhancing primary and secondary secrecy rates in cognitive radio networks when the ED can intercept both the primary and secondary transmission. Finally, this thesis focuses on physical-layer security in cognitive radio networks where multiple secondary nodes assist multiple primary nodes in combating unwanted eavesdropping from malicious eavesdroppers. Two scenarios are considered: a single eavesdropper (scenario I) and multiple eavesdroppers (scenario II). The secondary users act as a relay and jammer in scenario I, whereas they act only as a jammer in scenario II. Furthermore, the multiple eavesdroppers are distributed according to a homogenous Poison Point Process (PPP) in scenario II. Closed forms are derived for the outage probability and mean secrecy rate for both the primary and secondary transmissions. Furthermore, the scalability and convergence of the matching theory are proved. Both the analytical and numerical results show that the proposed matching model is a promising approach for exploiting the utility functions of both primary and secondary users.