As a revolutionary technology, reconfigurable intelligent surface (RIS) has been deemed as an indispensable part of the 6th generation communications due to its inherent ability to regulate the wireless channels. However, passive RIS (PRIS) still suffers from some pressing issues, one of which is that the fading of the entire reflection link is proportional to the product of the distances from the base station to the PRIS and from the PRIS to the users, i.e., the productive attenuation. To tackle this problem, active RIS (ARIS) has been proposed to reconfigure the wireless propagation condition and alleviate the productive attenuation. In this paper, we investigate the physical layer security of the ARIS assisted non-orthogonal multiple access (NOMA) networks with the attendance of external and internal eavesdroppers. To be specific, the closed-form expressions of secrecy outage probability (SOP) and secrecy system throughput are derived by invoking both imperfect successive interference cancellation (ipSIC) and perfect SIC. The secrecy diversity orders of legitimate users are obtained at high signal-to-noise ratios. Numerical results are presented to verify the accuracy of the theoretical expressions and indicate that: i) The SOP of ARIS assisted NOMA networks exceeds that of PRIS-NOMA, ARIS/PRIS-assisted orthogonal multiple access (OMA); ii) Due to the balance between the thermal noise and residual interference, introducing excess reconfigurable elements at ARIS is not helpful to reduce the SOP; and iii) The secrecy throughput performance of ARIS-NOMA networks outperforms that of PRIS-NOMA and ARIS/PRIS-OMA networks.