# GHEFL: Grouping Based on Homomorphic Encryption Validates Federated Learning
###### Abstract  
Federated learning is a powerful tool for securing participants' private data due to its ability to make data \"available but not visible\". In recent years, federated learning has been enhanced by the emergence of multi-weight aggregation protocols, which minimize the impact of erroneous parameters, and verifiable protocols, which prevent server misbehavior. However, it still faces significant security and performance challenges. Malicious participants may infer the private data of others or carry out poisoning attacks to compromise the model's correctness. Similarly, malicious servers may return incorrect aggregation results, undermining the model's convergence. Furthermore, substantial communication overhead caused by interactions between participants or between participants and servers hinders the development of federated learning. In response to this, this paper proposes GHEFL, a group-based, verifiable, federated learning method based on homomorphic encryption that aims to prevent servers from maliciously stealing participant privacy data or performing malicious aggregation. While ensuring the usability of the aggregated model, it strives to minimize the workload on the server as much as possible. Finally, we experimentally evaluate the performance of GHEFL. Keywords:data privacy; federated learning; verifiability; multi-servers; homomorphic encryption +
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enable model training and prediction while protecting user privacy [14]. With technological advancements, the application of federated learning has expanded to various fields. For instance, in the financial sector, federated learning is used for risk assessment [15; 16], fraud detection, and more. In the medical field [7], it facilitates disease prediction and drug development. In image recognition, federated learning supports tasks such as image classification [17] and object detection [18]. The FedSGD [10] and FedAvg [10] algorithms, proposed alongside the concept of federated learning, are the most fundamental and widely adopted in this field. FedSGD avoids uploading clients' raw data to servers by iteratively updating model parameters through gradient descent, thereby reducing the risk of data leakage. In contrast, FedAvg adopts a method of uploading model weights after local training to ensure client data security and reduce communication overhead. Since their introduction, numerous algorithms and frameworks for federated learning have been proposed. For example, [PERSON] et al. [19] proposed FedAsync, which enables asynchronous training updates without waiting for other clients' updates. [PERSON] et al. [20] introduced encryption mechanisms into federated learning by proposing SFL, allowing client model updates or gradients to remain encrypted during global aggregation. [PERSON] et al. proposed FedMA [21], which allows clients to generate local parameters using different models. The server then performs similarity matching on the parameters uploaded by the clients, thereby reducing the impact of noise and abnormal parameters on the global model parameters. In the FedProx algorithm [22], a proximal term is innovatively added to the local training function of the clients to limit the deviation between local and global parameters, accelerating model convergence. [PERSON] proposed FedDyn [23], which introduces a regularization coefficient and a Lagrange multiplier dynamically adjusted by the server into the local training function of the clients, enabling the local models to approximate the global model state and significantly improving the model training performance. To address the issues of client heterogeneity and data imbalance, [PERSON] et al. introduced the Layer-wise Adaptive Momentum Optimization (LAMB) algorithm into federated learning and proposed FedLamb [24]. By replacing traditional weighted averaging with layer-wise adaptive weighting, FedLamb ensures the stable and rapid convergence of the model even during large-batch training.