## 2 Related Work
### Privacy-Preserving Federated Learning  
Many solutions for preventing information leakage attacks have been proposed in recent years, to ensure that third parties cannot reconstruct the real training data. Common techniques used to research gradient protection include homomorphic encryption, differential privacy [11], and secure multiparty computation (SMC) [12]. Homomorphic encryption allows operations to be performed directly on ciphertext, yielding results in ciphertext form. Therefore, encrypted gradients can be aggregated over the ciphertext space, ensuring that gradients are not accessible to third parties. [PERSON] and [PERSON] [13] proposed the privacy-preserving federated learning algorithm, which enables the central server to aggregate encrypted model parameters. [PERSON] and [PERSON] [14] utilized an improved version of the Paillier encryption scheme to protect gradient information. [PERSON] et al. [15] encoded a batch of quantized gradients into a long integer and used homomorphic encryption for protection. [PERSON] et al. [16] adopted the concept of a multi-key homomorphic encryption protocol to encrypt gradients before aggregation on the server. [PERSON] et al. [17] designed a system in which, after the clients complete training, the fog nodes perform the first encryption, followed by a second encryption. While homomorphic encryption enables the aggregation of encrypted gradients, thereby preventing gradient leakage, it incurs substantial computational and storage costs. Differential privacy [11] was initially developed for protecting the privacy of databases. By slightly modifying the query result, the attacker cannot completely reconstruct the database content. [PERSON] et al. [18] used Gaussian differential privacy to build the federated learning scheme Noisy-FL, where noise is added before each round in which the server performs gradient averaging. [PERSON] et al. [19] implemented the addition of artificial noise to the client's parameters before aggregating them at the central server. [PERSON] and [PERSON] [20] applied Bayesian differential privacy to federated learning. LDP-FL [21] allows clients to perturb model weights with noise, divide and shuffle them, and then upload the weights to the central server for aggregation. While differential privacy is effective for protecting privacy, adding noise can impact the overall accuracy of a model. Balancing accuracy and privacy has always been a major concern in the context of differential privacy. SMC [12] is a technique in which a task is divided into subtasks, which are distributed to multiple parties. Once all subtasks are completed, their results can be merged to derive the result for the original task. Note that there is no leakage of the original task result when processing subtasks. There are many studies on applying SMC in federated learning. In federated learning with one cloud server and \(n\) clients, [PERSON] et al. [22] proposed that each client uses secret sharing to split gradients into \(n\) shares and send their shares to other clients, and clients then send the aggregated parameters to the server. In the Chain-PPFL scheme [23], a client generates a new token based on the trained model parameters and passes it to the next client, and the last client sends the token to the server, reflecting a chained-communication mechanism architecture. In federated learning with multiple servers and \(n\) clients, HybridAlpha [24] uses functional encryption for SMC to protect model gradients. [PERSON] et al. [7] introduced the SCOTCH framework. In a scenario with \(k\) servers and \(n\) clients, when the clients finish local training, SCOTCH divides each client's model into \(k\) shares via additive secret sharing, and each client sends the \(i\)-th share to the corresponding \(i\)-th server. The servers then sum the received shares and divide the total by the number of servers. Finally, the servers return the aggregated share to each client. [PERSON] et al. [8] extended the SCOTCH [7] framework and named it Fedshare [8].