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Physical Layer Security (PLS) for Uplink NonOrthogonal Multiple Access (UL-NOMA) is investigated, under cooperative multi-eavesdropping. Particular attention is paid to the effect that Successive Interference Cancellation (SIC) decoding order has over the system secrecy rate. Each NOMA user is subject to an individual minimum bit rate requirement, whereas multiple eavesdroppers cooperate among themselves to enhance their repercussion on the system. We demonstrate the impact SIC decoding order has on the secrecy performance, and the importance to look for an optimal solution to the decoding order selection problem. We show how this problem is indeed a very challenging combinatorial one with a factorial complexity related to the number of users and eavesdroppers involved in the system. Given the high computational power demand to find the optimal solution, we approach the challenge in two ways …