Energy efficiency and security are two critical issues for mobile edge computing (MEC) networks. With stochastic task arrivals, time-varying dynamic environment, and passive existing attackers, it is very challenging to offload computation tasks securely and efficiently. In this paper, we study the task offloading and resource allocation problem in a non-orthogonal multiple access (NOMA) assisted MEC network with security and energy efficiency considerations. To tackle the problem, a dynamic secure task offloading and resource allocation algorithm is proposed based on Lyapunov optimization theory. A stochastic non-convex problem is formulated to jointly optimize the local-CPU frequency and transmit power, aiming at maximizing the network energy efficiency, which is defined as the ratio of the long-term average secure rate to the long-term average power consumption of all users. The formulated problem is decomposed into the deterministic sub-problems in each time slot. The optimal local CPU-cycle and the transmit power of each user can be given in the closed-from. Simulation results evaluate the impacts of different parameters on the efficiency metrics and demonstrate that the proposed method can achieve better performance compared with other benchmark methods in terms of energy efficiency.
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