# GHEFL: Grouping Based on Homomorphic Encryption Validates Federated Learning
###### Abstract
These algorithms and frameworks have laid a solid foundation for the development and application of federated learning. Figure 1: The working process of federated learning. However, numerous studies have shown that although federated learning can protect users' private information to a certain extent, it still poses security risks. [PERSON] et al. (2018) highlighted the threat of inversion attacks, where an attacker exploits the confidence information from a client's model updates to reconstruct the private data used during training. [PERSON] et al. (2018) experimentally demonstrated the gradient leakage attack, wherein the gradients uploaded by participants may leak user data or private information related to the learning process. [PERSON] et al. (2018) showed that federated learning is vulnerable to Byzantine attacks during the data collection phase, where malicious participants disrupt the learning process, preventing the model from converging properly. In addition to security risks, federated learning is constrained by communication and computational resource limitations. [PERSON] et al. (2018) found that the frequent exchange of model updates between participants or with cloud servers introduces significant communication overhead, which can substantially impair the learning performance and convergence speed of federated learning. From the above analysis, it is evident that federated learning faces two primary challenges: security and efficiency. In federated learning, servers play a crucial role, and a malicious server that does not adhere to protocols can not only compromise the model's usability but also pose significant privacy threats to participants. During the data reception phase, a malicious server can act as an attacker, launching gradient leakage attacks on participants to infer sensitive information about their local data or learning process ([PERSON] et al., 2017). In the parameter aggregation phase, a malicious server may maliciously substitute a participant's model parameters with its own inputs without following the protocol ([PERSON] et al., 2017) or selectively aggregate participant model parameters, resulting in incorrect global model aggregation parameters. This, in turn, causes participants to receive unreliable models ([PERSON] et al., 2017). Moreover, federated learning also faces performance-related issues. As the number of participants and model parameters increases, the communication cost grows correspondingly ([PERSON] et al., 2017), which may lead to server overload in terms of computation and storage. This not only imposes an economic burden on participants but may also degrade server performance or even cause system crashes, ultimately impacting global model training. To address these challenges, various solutions have been proposed. [PERSON] et al. (2018) introduced VerifyNet, the first privacy-preserving and verifiable federated learning framework. Using a double-masking protocol, VerifyNet ensures that participants' local gradients remain confidential while enabling the cloud server to verify the correctness of aggregation results. However, the verification process is computationally intensive. [PERSON] et al. (2018) employed BLS signatures and secure multi-party computation to verify the correctness of server aggregation results. [PERSON] et al. (2018) proposed verifying aggregated gradients through Lagrangian interpolation points and optimized computational overhead using the Chinese Remainder Theorem (CRT). These schemes only partially address either security or performance issues individually. For example, while VerifyNet ensures the correctness of aggregation, its verification process requires substantial computational resources. In the scheme proposed by [PERSON] et al., the BLS signature and verification involve complex bilinear pairing operations, resulting in significant computational overhead and multiple interactions among participants, which adversely affect the efficiency of model training. Although the scheme proposed by [PERSON] et al.