We investigate the physical layer security of uplink single-carrier frequency-division multiple-access (SC-FDMA) systems. Multiple users, Alices, send confidential messages to a common legitimate base-station, Bob, in the presence of an eavesdropper, Eve. To secure the legitimate transmissions, each user superimposes an artificial noise (AN) signal on the time-domain SC-FDMA data block. We reduce the computational and storage requirements at Bob's receiver by assuming simple per-subchannel detectors. We assume that Eve has global channel knowledge of all links in addition to high computational capabilities, where she adopts high-complexity detectors such as single-user maximum likelihood (ML), multiuser minimum-mean-square-error (MMSE), and multiuser ML. We analyze the correlation properties of the time-domain AN signal and illustrate how Eve can exploit them to reduce the AN effects. We prove that the number of useful AN streams that can degrade Eve's signal-to-noise ratio (SNR) is dependent on the channel memories of Alices-Bob and Alices-Eve links. Furthermore, we enhance the system security for the case of partial Alices-Bob channel knowledge at Eve, where Eve only knows the precoding matrices of the data and AN signals instead of knowing the entire Alices-Bob channel matrices, and propose a hybrid scheme that integrates temporal AN with channel-based secret-key extraction.