In this paper, we investigate the physical-layer security of single-input single-output uplink single-carrier frequencydomain equalization (SC- FDE). A legitimate transmitter, Alice, sends confidential data messages to a legitimate receiver, Bob, in the presence of a passive eavesdropper, Eve. To secure her transmissions, Alice adds a time-domain artificial noise (AN) signal into each transmission block. The AN precoder is designed carefully to degrade Eve's receiver performance without affecting Bob's receiver performance. We investigate the impact of the transmit power allocation between data and AN signals on the average secrecy rate. Moreover, we consider three detection strategies at both Bob and Eve; namely, the zero-forcing (ZF) detector, linear minimum mean-square error (MMSE) detector and maximum likelihood (ML) detector. We investigate the correlation properties of the temporal AN symbols and illustrate if/how each detection strategy can exploit this correlation to reduce the AN effect on Eve. Furthermore, we highlight the tradeoffs between the complexities and average secrecy rates of the three detection strategies and we derive a closed-form expression for the average secrecy rate at high input SNR under the worse-case scenario when Eve performs ML detection.