# GHEFL: Grouping Based on Homomorphic Encryption Validates Federated Learning
## 4 The Proposed Scheme
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Solution** & **Techniques** & **Multi-Servers** & **Verifiable** & **Data Privacy** & **Security** & **Support for Participants** \\ \hline FedAvg & - & & & & & \\ G-VCFL & - & & & & & \\  & Secret Sharing & & & & & \\ VeriFL & + Homomorphic Hash & & & & & \\ VerifyNet & + Homomorphic & & & & & \\  & & & & & & \\ VERSA & Secret Sharing & & & & & \\ SASH & Secret Sharing & & & & & \\  & Secret Sharing & & & & & \\ GHEFL(This work) & + Homomorphic & & & & & \\  & Encryption & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison with federated learning works. successfully complete the final verification without gaining access to the information of other participants. * Low Interaction: In federated learning, it is common for the server to send masks to two participants, allowing one to obfuscate parameters for privacy protection using the mask while the other removes the mask's influence. This process incurs significant communication overhead, and when the number of participants is large, network bottlenecks become unavoidable. Additionally, the server must manage a large number of random values, resulting in a heavy workload. In this scheme, the server selects a random seed and transmits it only to the first user in each group, significantly reducing the information exchange between the server and participants and decreasing the server's workload in managing random values. Moreover, using the same random seed ensures consistency in random value generation across participants. Furthermore, having the last participant in each group secretly share the aggregated parameters with the dual servers also reduces communication interactions between participants and servers. ## 6 Conclusions

In this paper, we proposed a verifiable, group, and homomorphic encryption-based federated learning algorithm (GHEFL) that introduces a grouping mechanism, reducing the information exchange between participants and the server of traditional federated learning, and employs a dual-server architecture with homomorphic authentication to ensure user data privacy while guaranteeing the correctness and usability of model training. Additionally, the performance of GHEFL was evaluated on the MNIST dataset, and the experimental results demonstrate that this scheme improves both model accuracy and execution time compared to common privacy-preserving federated learning schemes. In future work, we will extend GHEFL to scenarios involving users with active attack capabilities or noise introduced during intermediate channel transmission to further optimize algorithm performance. In practical applications, different grouping strategies can be selected based on various scenarios, enabling GHEFL to be applied across multiple domains. When participant data exhibit strong heterogeneity, similar participants can be grouped together. For example, in the medical field, hospitals treating a specific disease can be grouped together, while in the financial sector, banking institutions with similar customer ratings can form a group. When participants have uneven computational resources, they can be grouped according to resource utilization. For instance, in the Internet of Things (IoT) domain, high-resource devices can be grouped together to undertake more computational tasks, thereby fully leveraging available resources. Considering real-world scenarios where participants may experience dropouts, high data heterogeneity, or varying requirements for privacy protection, as well as the potential for malicious participants to launch data poisoning attacks or model tampering attacks that disrupt model convergence, in future work, we will extend GHEFL to scenarios where participants can individually select models for local training or where users possess active attack capabilities. We will assign different weights to different participants to further optimize algorithm performance and accelerate model convergence.