# Privacy-Preserving Byzantine-Resilient Swarm Learning for E-Healthcare
## 7 Evaluation
### Experimental Results
#### 7.2.2 Efficiency Comparison with Related FL Approaches  
**Comparison of PBSL with alternative privacy protection schemes.** In the PBSL scheme, all operations, including similarity calculations and model aggregation, are computed in cipher-text. No participant can recover the original plaintext of the **MCs**\({}^{\prime}\) from the cipher-text. Therefore, the PBSL scheme meets the **MCs**\({}^{\prime}\) requirements for data privacy. To verify the efficiency of PBSL, using the Paillier-based federated learning scheme, i.e., PEFL [41], as a benchmark, we evaluated PBSL and BatchCrypt, where BatchCrypt [33] is a federated learning scheme based on HE. For each **MC**, we use the time required for encryption and decryption of each iteration as a criterion. As shown in Figure 7, PBSL greatly improves computational efficiency and reduces computational costs compared to baseline and BatchCrypt. PBSL adopts a novel encryption scheme, i.e., CKKS [34], which has its unique advantages in encrypting large-scale floating-point vectors and network models with many parameters.  
**Comparison of PBSL with alternative blockchain-based schemes.** Table 4 compares the model accuracy and mining overhead on the FashionMNIST dataset between LearningChain in [59], BCFL [45], and PBSL, where \(\alpha\) denotes training time per iteration and \(\beta\) denotes mining time per block. First, we observe that the proposed PBSL achieves the highest model accuracy, compared with LearningChain and BCFL. This is because the privacy protection of PBSL uses fully homomorphic encryption (FHE) instead of differential  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Scheme (Attacks)**} & \multicolumn{6}{c}{**\% of Malicious MCs**} \\ \cline{3-6}  & & **10**\% & **20**\% & **30**\% & **40**\% & **50**\% \\ \hline \multirow{4}{*}{**MNIST**} & PBSL (Untargeted) & 98.0 & 98.0 & 97.0 & 97.0 & 96.0 \\ \cline{2-6}  & Bulyan (Untargeted) & 97.0 & 95.0 & 94.0 & 80.0 & 58.0 \\ \cline{2-6}  & PBSL (Targeted) & 98.0 & 97.0 & 97.0 & 97.0 & 96.0 \\ \cline{2-6}  & Bulyan (Targeted) & 97.0 & 96.0 & 94.0 & 84.0 & 78.0 \\ \hline \multirow{4}{*}{**FashionMNIST**} & PBSL (Untargeted) & 87.0 & 87.0 & 86.0 & 85.0 & 85.0 \\ \cline{2-6}  & Bulyan (Untargeted) & 85.0 & 84.0 & 83.0 & 79.0 & 54.0 \\ \cline{2-6}  & PBSL (Targeted) & 88.0 & 88.0 & 87.0 & 87.0 & 86.0 \\ \cline{2-6}  & Bulyan (Targeted) & 87.0 & 87.0 & 85.0 & 80.0 & 72.0 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Accuracy of PBSL and Bulyan with different numbers of malicious MCs under untargeted attack and targeted attack on different datasets.  
Figure 7: Comparison of the cost time of encryption and decryption in baseline, BatchCrypt, and PBSL.  
privacy, which improves the accuracy of the model. Second, the mining overhead of PBSL is less than that of LearningChain but more than that of BCFL. This is due to the fact that LearningChain defends against Byzantine attacks at the cost of resource consumption for mining, while BCFL reduces the mining overhead at the expense of model robustness.  
And the model aggregation is implemented as functions of smart contract, and the computational cost of a function in a smart contract is assessed in gas units. Therefore, we measure the computational consumption of PBSL in gas. Using the CNN model, gas costs are tested in each iteration with 10 **MCs**. After all the **MCs** have submitted their local updates in cipher-text, SC obtains the global gradient at \(30,500,242\) gas per transaction by homomorphically aggregating all local updates.