## 5 Proposed Approach and System
### Threat Model  
Within our security framework, we acknowledge potential scenarios in which medical IoT devices could engage in adversarial behaviors by transmitting manipulated parameter updates to undermine the integrity of the aggregated model. Our analysis distinguishes between two critical vulnerabilities--namely, data exposure risks and model corruption attempts--which are thoroughly examined in subsequent sections. 1. Privacy leakage: In federated learning processes, compromised IoMT equipment may be able to deduce confidential data from legitimate participants. These adversarial actors could access gradient data submitted by compliant devices through blockchain records to reverse-engineer sensitive parameters. Contrary to protocol-following passive devices, maliciously active participants might alter intermediate computations within secure multiparty protocols. Furthermore, coordinated groups of IoMT devices could cooperate maliciously, amplifying their capacity to compromise the confidentiality of data. 2. Poisoning attacks: In the training phase, external adversaries might exploit compromised IoMT devices to initiate poisoning attacks. Attackers could potentially intercept sensitive details regarding localized training datasets and parameter adjustments from hijacked nodes. Simultaneously, they might intentionally distort the devices' optimization gradients to impede the collaborative learning model's stabilization process and degrade its predictive performance. We outline the workflow of the proposed protocol in Algorithm 1. Figure 4: System model. ```
1 Blockchain:
2:Task publisher publishes the initial parameters \(ipp\) by deploying an SC. 3:functionInitialization
4:IssueRegister() to all edge nodes. 5:Collect and verify all the \(proof_{sk}\). 6:endfunction
7:functionTrain
8:forepoch \(e=0,1,2,\cdots,E\)do
9:fortraining batch \(b=0,1,2,\cdots,B\)do
10:IssuePartial_Computation(\(e,b\)) to all the registered nodes
11:Collect the partial similarities \(\{[\xi_{i}^{(t)}]_{T}^{m}\}_{i\in[1,N]}\) from each node \(m\in[1,M]\)
12:Reconstruct all quantized similarities \(\{\xi_{i}^{(t)}\}_{i\in[1,N]}\) and convert to \(\{cs_{i}^{(t)}\}_{i\in[1,N]}\). 13:Compute the scores \(\{S_{i}^{(t)}=ReLU(cs_{i}^{(t)})\}_{i\in[1,N]}\) according to Equation (20). 14:IssuePartial_Aggregation(\(\{S_{i}^{(t)}\}_{i\in[1,N]}\)) to all nodes. 15:Collect the partial global gradients \(\{[\bar{\mathbf{g}}^{(t)}]_{T}^{m}\}_{m\in[1,T]}\) from each node \(m\). 16:Reconstruct the quantized global gradient \(\mathbf{g}^{(t)}\) based on Lagrange interpretation and convert to \(\mathbf{g}^{(t)}\). 17:end
18:end
19
20 end
216:endfunction
22 EdgeNode: \(m=1,2,\cdots,M\)
```  
```
1:RequestTA for \((h,p,q)\) and \(\{\theta_{m}\}_{m\in[1,M]}\). 2:functionRegister
3:Generate private/public key pair \(<sk_{m},pk_{m}>\)
4:\(proof_{sk_{m}}=prove(sk_{m},pk_{m})\)
5:Publish public key \(pk_{m}\) and \(proof_{sk_{m}}\) to the blockchain
6:endfunction
7:functionPartial_Computation(e,b)
8:Get global model \(\mathbf{w}^{(t-1)}\) from blockchain. 9:IssueLocalComputation(\(e,b,\mathbf{w}^{(t-1)}\)) to loMT devices. 10:Receive the secret shares \([\bar{\mathbf{g}}_{i}^{(t)}]_{T}^{m}\) and \(\{\mathbf{c}_{im}\}_{m\in[1,T]}\) from all devices \(i\in[1,N]\). 11:Verify the secret shares \(\{[\bar{\mathbf{g}}_{i}^{(t)}]_{T}^{m}\}_{i\in[1,N]}\) by \(\{\mathbf{c}_{im}\}_{i\in[1,N],m\in[1,T]}\)
12:Compute the partial similarities \(\{[\xi_{i}^{(t)}]_{T}^{m}\}_{i\in[1,N]}\)
13:Publish \(\{[\xi_{i}^{(t)}]_{T}^{m}\}_{i\in[1,N]}\) to the blockchain
14:endfunction
15:functionPartial_Aggregation(\(\{S_{j}^{(t)}\}_{j\in[1,N]}\))
16:Aggregate locally \([\bar{\mathbf{g}}_{i}^{(t)}]_{T}^{m}\) and \(\{S_{j}^{(t)}\}_{j\in[1,N]}\) to get \([\bar{\mathbf{g}}^{t}]_{T}^{m}\) according to Equation (22). 17:Publish \([\bar{\mathbf{g}}^{t}]_{T}^{i}\) to the blockchain. 18:endfunction
```  
_Devices: \(i=1,2,\cdots,N\)_  
```
1:functionLocalComputation(e,b,\(\mathbf{w}^{(t-1)},\))
2:\(\bar{\mathbf{g}}_{i}^{(t)}=ModelUpdate(e,b,\mathbf{w}^{(t-1)})\).