# A Review of Research on Secure Aggregation for Federated Learning
## 4 Aggregation Techniques for Federated Learning
### Secure Aggregation Algorithms
#### 4.2.2 Secure Aggregation Based on Secure Multi-Party Computation  
Secure multi-party computation addresses the collaborative computation challenge by splitting each local model into multiple secret shares and distributing them among participants. The aggregated model is then computed using these secret shares, ensuring privacy throughout the process. A schematic diagram of secure aggregation based on secure multi-party computation is shown in Figure 10. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type** & **Scheme** & **Algorithm** & **Protected Model** & **Network Structure** & **Resource Requirement** \\ \hline \multirow{8}{*}{Partially Homomorphic Encryption} & [65; 66; 67; 68; 69; 70; 71; 72] & Paillier & Local & Centralization & Acceptable \\  & [73] & ElGamal & Local & Centralization & Lightweight \\  & [74; 75] & threshold Paillier & Local & Centralization & High cost \\  & [76] & Joye-Libert & Local and Global & Centralization & Lightweight \\  & [77] & RSA/Paillier & Local & Trusted party & Acceptable \\  & [78; 79; 80] & threshold ElGamal & Local & Trusted party & Acceptable \\  & [81; 82] & Others & Local and Global & Centralization & High cost \\ \hline Fully Homomorphic Encryption & [83; 84; 85] & CKKS & Local and Global & Centralization & High cost \\  & [86; 87] & Others & Local & Centralization & High cost \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Secure aggregation schemes based on homomorphic encryption. Some previous works have investigated the privacy preservation of secure multi-party computation for machine learning. [PERSON] et al. [PERSON] _et al._ (2018) first introduced the concept of secure aggregation into federated learning by analyzing the security of prior methods and constructing SecAgg, a secure aggregation protocol based on [PERSON]'s secret sharing. Currently, secure aggregation for multi-party computation can be categorized into three types depending on the secret sharing scheme:  
**[PERSON]'s secret sharing**. Once [PERSON]'s secret sharing was applied to federated learning, several studies [PERSON] _et al._ (2018); [PERSON] _et al. results show that the protocol enhances privacy preservation while increasing the communication cost by only 0.04 times in a system with 100,000 users compared to previous schemes. In [94], federated learning is applied to the healthcare domain to predict patient severity. [PERSON]'s secret sharing is employed to ensure secure communication between clients and the edge aggregator. A dynamic edge thresholding mechanism is integrated, enabling an adaptive update strategy that can accept or reject model updates in real time. Experiments conducted on real-world ICU datasets (MIMIC-III) show that encryption of model updates increases computation time by approximately 50-60% per round and memory consumption by 35-40%. However, these overheads remain within a feasible range for real-world deployment. The accuracy degradation compared to the baseline scenario without secure multi-party computation is limited to 1-2 percentage points. **Verifiable secret sharing**. Most aggregation schemes based on secure multi-party computation focus on protecting local models, without considering the security of the global model. This limitation allows malicious servers to tamper with the global model, potentially reducing training efficiency and increasing the risk of exposing users' sensitive information. To verify the correctness of aggregation results returned by servers, several studies [95; 96; 97; 98] have proposed methods based on verifiable secret sharing schemes. The first privacy-preserving and verifiable federated learning framework, VerifyNet, was introduced in [95]. It ensures the confidentiality of users' local gradients during the federated learning process through a double-masking protocol. Additionally, it allows the cloud server to provide proof of the correctness of aggregation results, ensuring they are not tampered with.