Full-duplex communication enables simultaneous transmission from both ends of a communication link, thereby promising significant performance gains. Generally, it has been shown that the throughput and delay gains of full-duplex communication are somewhat limited in realistic network settings, leading researchers to study other possible applications that can accord higher gains. The potential of full-duplex communication in improving the physical-layer security of a communication link is investigated in this contribution. We specifically present a thorough analysis of the achievable ergodic secrecy rate and the secrecy degrees of freedom with full-duplex communication in the presence of a half-duplex eavesdropper node, with both single-user decoding and multi-user decoding capabilities. For the latter case, an eavesdropper with successive interference cancellation and joint decoding capabilities are assumed. Irrespective of the eavesdropper capabilities and channel strengths, the ergodic secrecy rate with full-duplex communication is found to grow linearly with the log of the direct channel SNR as opposed to the flattened out secrecy rate with conventional half-duplex communication. Consequently, the secrecy degrees of freedom with full-duplex is shown to be two as opposed to that of zero in half-duplex mode.