  This correspondence investigates a reconfigurable intelligent surface
(RIS)-assisted wireless communication system with security threats. The RIS is
deployed to enhance the secrecy outage probability (SOP) of the data sent to a
legitimate user. By deriving the distributions of the received
signal-to-noise-ratios (SNRs) at the legitimate user and the eavesdropper, we
formulate, in a closed-form expression, a tight bound for the SOP under the
constraint of discrete phase control at the RIS. The SOP is characterized as a
function of the number of antenna elements, $N$, and the number of discrete
phase choices, $2^b$. It is revealed that the performance loss in terms of SOP
due to the discrete phase control is ignorable for large $N$ when $b\!\geq\!3$.
In addition, we explicitly quantify this SOP loss when binary phase shifts with
$b\!=\!1$ is utilized. It is identified that increasing the RIS antenna
elements by $1.6$ times can achieve the same SOP with binary phase shifts as
that by the RIS with ideally continuous phase shifts. Numerical simulations are
conducted to verify the accuracy of these theoretical observations.
