  Although reconfigurable intelligent surface (RIS) can improve the secrecy
communication performance of wireless users, it still faces challenges such as
limited coverage and double-fading effect. To address these issues, in this
paper, we utilize a novel multi-functional RIS (MF-RIS) to enhance the secrecy
performance of wireless users, and investigate the physical layer secrecy
problem in non-orthogonal multiple access (NOMA) networks. Specifically, we
derive closed-form expressions for the secrecy outage probability (SOP) and
secrecy throughput of users in the MF-RIS-assisted NOMA networks with external
and internal eavesdroppers. The asymptotic expressions for SOP and secrecy
diversity order are also analyzed under high signal-to-noise ratio (SNR)
conditions. Additionally, we examine the impact of receiver hardware
limitations and error transmission-induced imperfect successive interference
cancellation (SIC) on the secrecy performance. Numerical results indicate that:
i) under the same power budget, the secrecy performance achieved by MF-RIS
significantly outperforms active RIS and simultaneously transmitting and
reflecting RIS; ii) with increasing power budget, residual interference caused
by imperfect SIC surpasses thermal noise as the primary factor affecting
secrecy capacity; and iii) deploying additional elements at the MF-RIS brings
significant secrecy enhancements for the external eavesdropping scenario, in
contrast to the internal eavesdropping case.
