## 5 Proposed Approach and System
### Local Computation
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Schemes**} & **Resisting** & **Privacy** & **Poisoning** & **Light-** & **Security** \\  & **Against SPOF** & **Protection** & **Defense** & **Weight Comp.** & **Level** \\ \hline SL & \(\surd\) & \(\times\) & \(\times\) & – & – \\ \cline{1-1}
[10] & (Blockchain) & & & & \\ \hline SL+HE & \(\surd\) & \(\surd\) & \(\times\) & \(\times\) & Passive \\
[15] & (Blockchain) & (Paillier) & & & \\ \hline Learning & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & Passive \\ Chain [25] & (Blockchain) & (DP) & & & \\ \hline PPML & \(\surd\) & \(\surd\) & \(\times\) & – & Passive \\
[16] & (Single-Server) & (SMC) & & & \\ \hline Securen & \(\surd\) & \(\surd\) & \(\times\) & \(\times\) & Passive \\
[29] & (Triple-Server) & (SMC) & & & \\ \hline Krum & \(\times\) & \(\times\) & \(\surd\) & – & – \\
[17] & (Single-Server) & & & & \\ \hline FLTrust & \(\times\) & \(\times\) & \(\surd\) & – & – \\
[31] & (Single-Server) & & & & \\ \hline BFLC & \(\surd\) & \(\times\) & \(\surd\) & – & – \\
[24] & (Blockchain) & & & & \\ \hline Bit & \(\surd\) & \(\times\) & \(\surd\) & – & – \\
[33] & (Blockchain) & & & & \\ \hline Our & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & Active \\ Scheme & (Blockchain) & (SMC) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: A comparative summary between our scheme and previous schemes. * Verifiability of the Global Model: As a decentralized technology, blockchain can maintain the integrity of data. In our PPBFL, we leverage blockchain to store the latest global model after the secure aggregation process. The decentralized process makes it impossible for adversaries to tamper with or alter the global model, as this will change the hash value. Later, the global model stored in the blockchain will be sent to the IoMT devices. Moreover, the devices can verify the integrity of the global model by checking the signatures and hashes before they use it. ## 10 Conclusions

In this study, we proposed a privacy-preserving blockchain-based federated learning (BFL) framework that protects against poisoning attacks, thus promoting safe data sharing in the IoMT context. In particular, the PPBFL was constructed to address the contradictory issues of privacy protection and poisoning defense in BFL. Based on the actively secure evaluation protocol and hierarchical framework, our PPBFL is characterized by its security, utility, robustness, and efficiency, effectively satisfying the demands of practical IoMT. In the proposed framework, we provide a privacy-preserving training mechanism using a \((T,N)\)-threshold MPC-based scheme, which ensures low computation and communication overheads. To resist poisoning attacks, we provide a robust global model by filtering out the harmful gradients using the cosine similarity. Our key insight is that the cosine similarity can be calculated homomorphically, based on our actively secure evaluation protocol, thus making it feasible to simultaneously ensure privacy protection and poisoning defense in FL. Furthermore, the blockchain is used to facilitate transparent processes and the enforcement of regulations, eliminating the need for a central coordinating authority during model training processes. Experiments were carried out on two medical datasets--PathMNIST [36] and OCTMNIST [37] --allowing for comparison of the proposed approach with Swarm Learning (SL) [10] and Krum [17]. The experimental results demonstrated that the proposed scheme can resist model poisoning attacks and achieve high global model accuracy. In the future, we plan to develop an efficient consensus mechanism for PPBFL, in order to reduce computational and energy resources, as well as an incentive mechanism for PPBFL, in order to drive participants to actively and honestly take part in FL training tasks. Meanwhile, we plan to broaden the scope of PPBFL in the future in order to better support heterogeneous models in blockchain-based federated learning (BFL) for data sharing in IoMT.