## 1 Introduction  
The Internet of Medical Things (IoMT)--a subset of the Internet of Things (IoT)--comprises interconnected smart medical devices, wearable health gadgets, and other medical hardware [1, 2]. The widespread adoption of IoMT enables the continuous transfer and exchange of patient medical data among medical institutions, healthcare professionals, devices, and applications. However, due to competitive pressures, medical institutions are often reluctant to share their medical data with others. The transmission of patient health information, which includes sensitive personal and institutional details, poses risks to individual privacy, institutional security, and potentially national security. To overcome these challenges and harness the full potential of IoMT data, secure and trusted data sharing approaches are urgently needed. Federated learning (FL) represents an innovative approach to machine learning that enables joint model development across decentralized datasets owned by multiple devices, while ensuring that the data are still stored on local devices [3]. This framework achieves knowledge exchange through the periodic aggregation of updated model parameters from participating devices. However, existing federated learning frameworks still face security vulnerabilities, particularly due to the centralized server architecture's susceptibility to targeted attacks on critical nodes, which may result in unauthorized access to sensitive training datasets [4]. Blockchain's decentralization, immutability, and traceability [5] have been leveraged for integration with FL frameworks for model parameter aggregation, replacing the traditional central server [6; 7]. Blockchain-based federated learning (BFL) enhances the reliability and scalability of FL by mitigating single points of failure (SPFs) and improving communication efficiency [8; 9]. [PERSON] et al. [10] introduced a BFL approach called Swarm Learning (SL), which combines blockchain and FL to collaboratively train models for the diagnosis of multiple diseases while safeguarding patient data privacy and security. However, maintaining gradient data as transactional entries within BFL systems can create security vulnerabilities. Studies have revealed that malicious actors infiltrating blockchain records could launch inference-based assaults to reconstruct sensitive training datasets from exposed gradients [11]. To mitigate these risks, privacy-preserving federated learning (PPFL) frameworks have gained substantial attention across research and industrial domains [12]. The PPFL framework predominantly employs three core methodologies: differential privacy (DP) mechanisms, homomorphic encryption (HE) protocols, and secure multi-party computation (MPC) techniques. [PERSON] [13] combines DP with secure aggregation protocols [14] to fortify BFL architectures against both data poisoning attempts and gradient-based inference breaches. [PERSON] et al. [15] illustrated how swarm learning updates can implement partial HE to safeguard BFL systems from inference threats, although this method suffers from operational inefficiencies due to computational complexities in cipher-text processing. MPC-based privacy preservation [16] achieves data indistinguishability through secret sharing mechanisms, but requires significant communication resources due to intensive client-server coordination demands. However, existing PPFL methods primarily ensure the indistinguishability of private information while often neglecting the threat of adversarially manipulated gradients. Attackers can craft malicious gradients to undermine aggregation results and disrupt the training process. Several aggregation rules have been developed to counteract poisoning attacks [17; 18; 19], which filter out malicious gradients by distinguishing them from legitimate ones. For example, Krum [17] identifies and excludes poisonous gradients by measuring their Euclidean distance from benign gradients.