# A Review of Research on Secure Aggregation for Federated Learning
## 4 Aggregation Techniques for Federated Learning
### Secure Aggregation Algorithms
#### 4.2.1 Secure Aggregation Based on Homomorphic Encryption
Regarding computational overhead, it introduces only a linear increase proportional to the number of parameters. **Fully Homomorphic Encryption**. In [83; 84; 85; 86; 87], fully homomorphic encryption is also performed on the global model for federated learning to further protect the global model rather than just the local model. In this case, the global model is encrypted for the user, who needs to train their model on the ciphertext, which requires multiplicative homomorphic operations in addition to additive homomorphic operations. This necessitates fully homomorphic encryption systems capable of supporting these operations. **Hybrid Scheme**. Refs. [81; 82] propose combining homomorphic encryption with other privacy-preserving mechanisms to make federated learning more adaptable to various scenarios. For example, Ref. [81] combines differential privacy with homomorphic encryption, proposing a new multi-party learning framework for privacy preservation in vertically partitioned environments. The core idea leverages the functional mechanism, addressing the challenge of applying differential privacy in vertically partitioned scenarios. This is achieved by adding noise to the objective function. Experiments demonstrate that for linear regression, the scheme achieves a mean square error of 0.007, which is very close to the 0.0044 of privacy-preserving linear regression. For logistic regression, the scheme's utility deteriorates as the privacy budget decreases, achieving an accuracy of 0.8132 \(\pm\) 0.0231 when the privacy budget is 10, approximating privacy-preserving logistic regression. In [82], secure multiparty computation is combined with homomorphic encryption to implement the scheme in a cloud-based federated learning service scenario. However,the appropriate number of clients must be carefully determined, as the communication overhead increases when the server and clients use encrypted model vectors to protect model parameters. Experiments show that the computational overhead of the baseline algorithm in the same scenario is 2.3 times higher than this scheme. The key size of homomorphic encryption significantly impacts runtime. Combining it with other privacy-preserving mechanisms can result in high computational overhead, highlighting the need to balance security and computational efficiency. Partially homomorphic encryption offers faster encryption and decryption, low communication overhead, and minimal impact on model accuracy. For example, Refs. [73; 76] demonstrates lower communication costs and computational overhead compared to [83], while achieving higher model accuracy. However, Ref. [76] does not support multiplication operations and is, therefore, unsuitable for complex model updates. Generally, fully homomorphic encryption incurs longer training times per round and higher communication costs, making it unsuitable for edge deployments. Nevertheless, it provides strong security guarantees, supports complex computations, and ensures controllable accuracy degradation. For example, Ref. [83] defends against N-1 attacker inference, reconstruction attacks, and membership inference, whereas Ref. [73] fails to defend against malicious clients tampering with model updates. Hybrid encryption schemes can mitigate accuracy loss through mechanisms such as differentially private balancing. They typically incur moderate communication costs, which can be further reduced using compression or pruning techniques. For example, Ref. [81] incurs lower communication costs and computational overhead than [76], but achieves lower model accuracy. However, these schemes tend to be more complex to implement and less practical in real-world deployment scenarios. In this paper, secure aggregation schemes based on homomorphic encryption are categorized into partially and fully homomorphic encryption, as summarized in Table 1.