In this paper, we construct two repairable threshold schemes (RTSs) using a resolvable balanced incomplete block design (RBIBD). First, a resolvable transversal design is given by mutually orthogonal Latin squares. Further, a RBIBD is obtained through the filling hole method, and two repairable key sharing threshold schemes based on the Ramp threshold scheme are constructed based on this design. Finally, the information rate, the repairing degree and the communication complexity of two RTSs are calculated, and the performance of the schemes is analyzed. Compared with the existing schemes, the results show that two schemes constructed in this paper have a higher information rate, a larger repairing degree and lower communication complexity.

The interconnected nature of the Internet of Things (IoT) significantly enhances the efficiency of industries such as smart manufacturing, but it also raises concerns about data privacy. Federated learning (FL) utilizes an edge-cloud collaborative mode that shares models in the cloud instead of data, effectively mitigating data privacy leakage in edge IoT devices. However, FL suffers from the risk of model leakage, and both the cloud and the edge may illegally copy and sell the model, infringing on model ownership. To prevent such misbehavior, it is essential to design a robust method for verifying the model ownership. In this paper, we propose Fed-RWM, a novel watermarking method for FL models that provides robust ownership verification and avoids both edge and cloud leakage of watermark information. Fed-RWM trains the watermark by sharing parameters with an additional model and incorporates a watermark recovery method during verification to counter complex watermark removal attacks, which enhances the verification robustness. Fed-RWM introduces a new training paradigm that performs continuous watermarking training at the FL task initiator, preventing access to watermark information at both the edge and the cloud. The experimental results demonstrate that Fed-RWM performs well in model ownership verification and fidelity, is robust to different watermark removal attacks, and can provide reliable protection for federated learning models.