  In this paper, we propose an opportunistic user scheduling scheme in a
multi-user reconfigurable intelligent surface (RIS) aided wireless system to
improve secrecy. We derive the secrecy outage probability (SOP) and its
asymptotic expression in approximate closed form. The asymptotic analysis shows
that the SOP does not depend on the transmitter-to-RIS distance and saturates
to a fixed value depending on the ratio of the path loss of the
RIS-to-destination and RIS-to-eavesdropper links and the number of users at
high signal-to-noise ratio. It is shown that increasing the number of RIS
elements leads to an exponential decrease in the SOP. We also compare our
scheme with that of a non-orthogonal multiple access (NOMA) scheduling scheme,
which chooses a pair of users to schedule in each time slot. The comparison
shows that the SOP of all of the NOMA users is compromised, and that our
proposed scheduling scheme has better performance.
