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The effects of hardware impairments (HWIs) on the secrecy performance of a reconfigurable intelligent surface (RIS)-assisted millimeter wave system are investigated, where a multi-antenna base station (BS) transmits confidential messages to a single-antenna mobile user (MU) in the presence of a single-antenna passive eavesdropper (Eve). Artificial noise (AN)-aided transmission by the BS is proposed for improving the achievable secrecy rate. As the first step, we construct a system model in the absence of HWIs. For this case, we present optimal solutions for the signal and AN powers, the beamforming design at the BS, and the phase shifts of the RIS elements. Then closed-form expressions are derived for the cumulative distribution functions of the signal-to-noise-ratios experienced at the legitimate and eavesdropping nodes. Finally, a compact solution is presented for the ergodic secrecy rate (ESR) performance. At the next step, we extend our designs and analysis by considering the HWIs of the radio-frequency (RF) modules of the BS, MU and Eve. Our results highlight the detrimental impact of HWIs on the achievable ESR. Finally, we find that the ESR can be further increased by beneficially distributing the tolerable HWIs between the transmission and reception RF chains.