In this paper, we investigate the secrecy performance of dual-hop randomize-and-forward (RaF) cognitive wiretap networks over Rayleigh fading channels, in which the RaF relay is considered both as half-duplex (HD) and full-duplex (FD) operations. Specifically, for the HD, maximal-ratio combining/maximal-ratio transmission (MRC/MRT) is adopted at the RaF relay. For the FD, the RaF relay can simultaneously receive the signal from the source and transmit jamming signals to eavesdropper, and the selection combining-zero forcing beamforming/maximal-ratio transmit (SC-ZFB/MRT) and SC-ZFB/ZFB schemes are respectively adopted at the FD relay. To thoroughly assess the secrecy performance achieved from the proposed schemes, the closed-form expressions for the secrecy outage probability (SOP) of the dual-hop RaF cognitive wiretap channels with MRC/MRT, SC-ZFB/MRT and SC-ZFB/ZFB schemes are derived, respectively. In addition, we also provide simple asymptotic approximations for the SOP under two distinct scenarios, depending on the quality of the main and wiretap channels. Additionally, our analytical results and numerical simulations show the efficiency of our proposed solutions for both SC-ZFB/MRT and SC-ZFB/ZFB with FD cases and show considerable performance gains over MRC/MRT with HD scheme. Finally, for the proposed schemes, the SC-ZFB/ZFB scheme is beneficial to improve secrecy performance when the eavesdropper's channel is better than the main channel and the RaF relaying strategy achieves better secrecy performance than that of the decode-and-forward (DF) relaying strategy for dual-hop cognitive wiretap networks. INDEX TERMS Physical layer security, cognitive radio, full duplex, multiple antennas relay, secrecy outage probability, zero forcing beamforming (ZFB).