# Efficient and Secure Federated Learning for Financial Applications
## 6 Conclusions  
In this paper, we present our research findings on the application of sparsity to secure aggregation in federated learning. Our main contributions are:  
* We propose an efficient and secure FL framework that can significantly reduce the communication costs of a single communication while ensuring privacy.
* Our proposed framework results in fewer model performance losses than the traditional sparsity method.
* Experiments conducted under various non-IID experimental settings demonstrate that the proposed algorithm can reduce the upload communication costs to about 2.9% to 18.9% of the conventional FL algorithm when the sparsity rate is 0.01.  
Overall, our research demonstrates the potential benefits of incorporating sparsity into federated learning and presents a promising approach for achieving better communication efficiency while maintaining data privacy and model performance.  
Future work could involve adding gradient correction, batch-normalized updates, and local gradients to the sparse gradient update process to maintain model accuracy after high-ratio sparsification. Additionally, adaptive sparsity could be used to automatically control the trade-off between optimal communication and computation. In terms of security aggregation, a DH key exchange before each round of training may increase the training time. Although the sparse mask matrix is conducive to increasing the training speed,  
Figure 4: Comparison with state-the-of-art methods.  
the extra time needed for the DH key exchange may affect the overall communication optimization. This aspect needs to be further studied.  
Conceptualization, T.L.; methodology, Z.W.; software, H.H.; investigation, W.S.; data curation, L.L.; writing--original draft preparation, R.A.; writing--review and editing, C.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by NSFC grant number 62176205.  
Not applicable.  
The authors conduct classification experiments using three public datasets, i.e., MNIST ([[http://yann.lecun.com/exdb/mnist/](http://yann.lecun.com/exdb/mnist/)]([http://yann.lecun.com/exdb/mnist/](http://yann.lecun.com/exdb/mnist/)) (accessed on 24 November 2022)), Fashion-MNIST ([[https://github.com/zalandoresearch/fashion-mnist](https://github.com/zalandoresearch/fashion-mnist)]([https://github.com/zalandoresearch/fashion-mnist](https://github.com/zalandoresearch/fashion-mnist)) (accessed on 24 November 2022), or [30]) and CIFAR-10 ([[http://www.cs.toronto.edu/kriz/cifar-10-matlab.tar.gz](http://www.cs.toronto.edu/kriz/cifar-10-matlab.tar.gz)]([http://www.cs.toronto.edu/kriz/cifar-10-matlab.tar.gz](http://www.cs.toronto.edu/kriz/cifar-10-matlab.tar.gz)) (accessed on 24 November 2022)).  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} ML & Machine learning \\ FL & Federated learning \\ CNN & Convolutional neural networks \\ DP & Differential Privacy \\ HE & Homomorphic Encryption \\ SMC & Secure Multiparty Computation \\ SA & Secure Aggregation \\ DGC & Deep gradient compression \\ STC & Sparse compression framework \\ THGS & Time-varying hierarchical gradient sparsification \\ \end{tabular}