# 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
Experimental results show that training a convolutional neural network on the MNIST dataset, with 500 users and a total of 500,000 gradients, requires 70 MB per user for a single parameter update iteration. In [96], a non-interactive, verifiable, and decentralized federated learning scheme was proposed. This scheme decentralizes the process by splitting users' secret inputs and distributing them to multiple servers. A subset of these servers collaborates to correctly reconstruct the outputs, ensuring the results are not tampered with. Experiments demonstrate that this approach enables distributed aggregation of secret inputs across multiple untrusted servers and outperforms prior methods. To enhance the efficiency of federated learning while reducing communication, computational, and storage costs for low-resource devices, Refs. [97; 98] proposed optimizations that maintain the confidentiality of users' local gradients and verify aggregation results. Experimental results indicate that the schemes reduce device power consumption due to lightweight computation. In [99], a verifiable federated learning scheme was designed to protect sensitive training data in industrial IoT environments and prevent malicious servers from returning falsified aggregated gradients. This scheme employs Lagrangian interpolation, carefully setting interpolation points to verify the correctness of aggregated gradients. By combining Lagrangian interpolation with blinding techniques, it achieves secure gradient aggregation. Notably, the scheme maintains a constant validation overhead compared to existing methods, regardless of the number of participants. **Additive secret sharing**. The traditional secret sharing scheme uses Shamir's secret sharing, which splits the secret into multiple shares based on polynomial interpolation and recovers the secret through Lagrange polynomials. However, this algorithm has high computational and communication costs, so some research efforts have focused on lightweight improvements [100; 101; 102; 103; 104; 105]. Among them, Refs. [100; 101] focus on preventing information leakage in centralized federated learning systems and adopt encryption methods that differ from traditional schemes. In [100], a partial encryption method is used, encrypting only the first layer of the local model with additive secret sharing, while the rest is sent directly to the central server. Experiments show that the secret share generation time decreases from 2.7081 s to 0.6951 s and the secret share aggregation time decreases from 0.0019 s to 0.0008 s compared to applying secret sharing to the entire local model. Ref. [101] focuses on training split models in a vertical federated learning scenario. To address performance degradation caused by client discretization and privacy leakage from client-embedded information, the FedVS framework for synchronous split vertical federated learning is proposed, which reconstructs the set of user embeddings in a lossy manner by designing an additive secret sharing scheme. Experiments show that this framework guarantees user privacy and improves performance in scenarios with discrete clients compared to baseline methods. Refs. [102; 103] study decentralized federated learning systems based on secure multi-party computation, exploring optimizations from different perspectives to achieve high accuracy, low communication costs, and scalability without compromising privacy. In [102], the optimization of the additive secret sharing algorithm is considered by replacing the secure summation building block from [106] with the secure summation algorithm from [107], simplifying the protocol while eliminating the need for public key encryption. Considering client selection prior to aggregation, Ref. [103] proposes a hierarchical mechanism based on secure multi-party computation that restricts model aggregation to a small number of aggregation committee members. Experiments demonstrate a 90% reduction in exchanged messages on the MNIST dataset and a 22% accuracy improvement compared to locally trained models.