For the sake of improving the physical-layer security, reconfigurable intelligent surface (RIS) has been suggested to assist artificial noise (AN) to bridge both their advantages in multiple-input single-output (MISO) systems. Specifically, for achieving the trade-off between the reliability and security of transmission, the phase shifts (PSs) and beamforming are jointly designed based on the oblique manifold (OM) algorithm (Wang et al., 2020) without eavesdropper’s channel state information (CSI). In order to alleviate the computational complexity, a novel alternating direction (AD) algorithm is proposed in this contribution. Specifically, the initial problem is transformed into several subproblems, each of which determines a specific RIS unit via a closed-form solution when the other configurations are fixed. Furthermore, the AD algorithm is investigated to exhibit the low-complexity advantage in contrast to OM. Simulation results illustrate that AD can converge faster and more stably compared to OM with the same performance.