Digital twin has been emerging as a promising paradigm that connects physical entities and digital space, and continuously evolves to optimize the physical systems. In this article, we focus on studying efficient communication and computation scheme when constructing the Marine Internet of Things (M-IoT)'s digital twin with secrecy provisioning. Specifically, the digital twin model is trained based on federated learning, in which all the unmanned surface vehicles deliver the trained models with nonorthogonal multiple access (NOMA) to the high-altitude platform (HAP) for global model aggregation. Considering the potential eavesdropping on the radio signals of HAP, we utilize the chaotic sequences to spread the model information before the global model broadcasting. In this framework, we aim to minimize the total energy consumption for constructing the digital twin of M-IoT by jointly optimizing the global accuracy, the local accuracy, the HAP's transmission power and NOMA transmission duration, subject to the secrecy provisioning and latency constraint. An effective low-complexity algorithm is proposed to tackle this joint optimization problem with the use of a layered feature. Finally, numerical results are given to validate the performance gain of the proposed scheme, in comparison with the fixed accuracy scheme, the nonspread spectrum scheme and the time division multiple access transmission scheme.