The dual-functional radar and communication (DFRC) technique constitutes a promising next-generation wireless solution, due to its benefits in terms of power consumption, physical hardware, and spectrum exploitation. In this paper, we propose sophisticated beamforming designs for multi-user DFRC systems by additionally taking the physical layer security (PLS) into account. We show that appropriately designed radar waveforms can also act as the traditional artificial noise conceived for drowning out the eavesdropping channel and for attaining increased design degrees of freedom (DoF). The joint beamforming design is formulated as a non-convex optimization problem for striking a compelling trade-off amongst the conflicting design objectives of radar transmit beampattern, communication quality of service (QoS), and the PLS level. Then, we propose a semidefinite relaxation (SDR)-based algorithm and a reduced-complexity version to tackle the non-convexity, where the globally optimal solutions are found. Moreover, a robust beamforming method is also developed for considering realistic imperfect channel state information (CSI) knowledge. Finally, simulation results are provided for corroborating our theoretical results and show the proposed methods' superiority.