  Mobile edge computing (MEC) has been envisaged as a promising technique in
the next-generation wireless networks. In order to improve the security of
computation tasks offloading and enhance user connectivity, physical layer
security and non-orthogonal multiple access (NOMA) are studied in MEC-aware
networks. The secrecy outage probability is adopted to measure the secrecy
performance of computation offloading by considering a practically passive
eavesdropping scenario. The weighted sum-energy consumption minimization
problem is firstly investigated subject to the secrecy offloading rate
constraints, the computation latency constraints and the secrecy outage
probability constraints. The semi-closed form expression for the optimal
solution is derived. We then investigate the secrecy outage probability
minimization problem by taking the priority of two users into account, and
characterize the optimal secrecy offloading rates and power allocations with
closed-form expressions. Numerical results demonstrate that the performance of
our proposed design are better than those of the alternative benchmark schemes.
