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This paper examines linear beamforming methods for secure communications in a multiuser wiretap channel with a single transmitter, multiple legitimate receivers, and a single eavesdropper, where all nodes are equipped with multiple antennas. No information regarding the eavesdropper is presumed at the transmitter, and we examine both the broadcast MIMO downlink with independent information, and the multicast MIMO downlink with common information for all legitimate receivers. In both cases the information signal is transmitted with just enough power to guarantee a certain SINR at the desired receivers, while the remainder of the power is used to broadcast artificial noise. The artificial interference selectively degrades the passive eavesdropper's signal while remaining orthogonal to the desired receivers. We analyze the confidentiality provided by zero-forcing and optimal minimum-power beamforming designs for the broadcast channel, and optimal minimum-MSE beamformers for the multicast channel. Numerical simulations for the relative SINR and BER performance of the eavesdropper demonstrate the effectiveness of the proposed physical-layer security schemes.