  This paper investigates the security enhancement of an intelligent reflecting
surface (IRS) assisted non-orthogonal multiple access (NOMA) network, where a
distributed IRS enabled NOMA transmission framework is proposed to serve users
securely in the presence of a passive eavesdropper. Considering that
eavesdropper's instantaneous channel state information (CSI) is challenging to
acquire in practice, we utilize secrecy outage probability (SOP) as the
security metric. A problem of maximizing the minimum secrecy rate among users,
subject to the successive interference cancellation (SIC) decoding constraints
and SOP constraints, by jointly optimizing transmit beamforming at the BS and
phase shifts of IRSs, is formulated. For special case with a single-antenna BS,
we derive the exact closed-form SOP expressions and propose a novel
ring-penalty based successive convex approximation (SCA) algorithm to design
power allocation and phase shifts jointly. While for the more general and
challenging case with a multi-antenna BS, we adopt the Bernstein-type
inequality to approximate the SOP constraints by a deterministic convex form.
To proceed, an efficient alternating optimization (AO) algorithm is developed
to solve the considered problem. Numerical results validate the advantages of
the proposed algorithms over the baseline schemes. Particularly, two
interesting phenomena on distributed IRS deployment are revealed: 1) the
secrecy rate peak is achieved only when distributed IRSs share the reflecting
elements equally; and 2) the distributed IRS deployment does not always
outperform the centralized IRS deployment, due to the tradeoff between the
number of IRSs and the reflecting elements equipped at each IRS.
