Federated learning (FL) has been considered as an efficient yet privacy-preserving approach for enabling the distributed learning. There have been many studies investigating the applications of FL in different scenarios, e.g., Internet of Things, Internet of Vehicles, and UAV systems. However, due to delivering the trained model via wireless links, FL may suffer from a potential issue, i.e., some malicious users may intentionally overhear the trained model delivered through the wireless links. In this paper, we investigate the energy optimization for nonorthogonal multiple access (NOMA) assisted with secrecy provisioning. Specifically, we consider that the wireless devices (WDs) adopt NOMA to deliver their respectively trained local models to a base station (BS) which serves a parameter-server, and there exists a malicious node that overhears the parameter-server when delivering the aggregated global model to all WDs. We adopt the physical layer security to quantify the secrecy throughput under the eavesdropping attack and formulate an optimization problem to minimize the overall energy consumption of all the WDs in FL, by jointly optimizing the uplink time, the downlink time, the local model accuracy, and the uplink decoding order of NOMA. In spite of the non-convexity of this joint optimization problem, we propose an efficient algorithm, which is based on the theory of monotonic optimization, for finding the solution. Numerical results show that our proposed algorithm can achieve the almost same solutions as the LINGO's global-solver while reducing more than 90% computation-time than LINGO. Moreover, the results also show that our proposed NOMA decoding scheme can outperform some heuristic decoding schemes.