# GHEFL: Grouping Based on Homomorphic Encryption Validates Federated Learning
## 4 The Proposed Scheme
After each round of federated learning training, the test set was used to evaluate the model performance, and curves depicting the accuracy of different schemes as a function of communication rounds were plotted to observe the model accuracy of the different schemes. Figure 5a and Figure 5b respectively show the total execution time required for each scheme's model to converge under noise levels of 0.2 and 0.5. It can be observed from the figures that as the noise scale increased, the execution time required by the GHEFL scheme rose to a certain extent, but it remained lower than that of the other two protocols. Therefore, GHEFL has better operational efficiency. Figure 6 presents an evaluation of the resistance to attacks for four federated learning schemes, including GHEFL. A server model tampering attack was employed, where Gaussian noise with a variance of 0.2 was added to the parameters when the server returned the globally aggregated parameters. Attacks were conducted on 20% to 50% of the partic



### Functionality

In order to evaluate the performance of GHEFL as comprehensively as possible, we compared GHEFL with state-of-the-art privacy-preserving federated learning solutions. The results are shown in \[w_{1}^{*}=w_{1}-r_{i},\]2 As the most basic and common federated learning framework, FedAvg ensures the efficiency of model training but lacks data protection measures, making it susceptible to attacks and unable to address the security issues raised in this scheme. Although G-VCFL supports participant dropout and meets the requirements for verifiability, it allows participants within the same group to obtain locally aggregated parameters, which may potentially lead to the acquisition of data from other participants. Furthermore, the server must send pseudo-random numbers to the first and last participants in each subgroup, leading to significant communication overhead and difficulty in managing a large number of stored random numbers. VerifyNet, VeriFL, and VERSA meet participants' needs to verify aggregation results, but their verification processes involve extensive user interactions, resulting in high communication overhead. Additionally, their single-server architectures are prone to network latency issues when the number of participants increases. SASH adopts a dual-server architecture, ensuring global model accuracy while protecting participants' data privacy. However, it does not support participant dropout and lacks verifiability, preventing participants from confirming the correctness of the training model. Since GHEFL is a verifiable secure aggregation scheme, its design focus is on ensuring data privacy. As a result, it does not support participant dropout. However, GHEFL also addresses some limitations of existing schemes to a certain extent. While protecting user data privacy, it strives to reduce reliance on high bandwidth and improve the efficiency of model training. ### Theoretical Evaluation

* Security: The security mechanism of the verification protocol in this scheme relies on the dual-server architecture and the security guarantees provided by cryptographic techniques, specifically secret sharing and homomorphic encryption. The dual-server architecture, combined with the security of secret sharing, ensures that even if both servers act maliciously and collude, they cannot obtain or tamper with the local model parameters and related information of any participant. Furthermore, the homomorphic and one-way properties of homomorphic encryption ensure that each participant can