# Efficient and Secure Federated Learning for Financial Applications
## 1 Introduction
The reason is that the residual of the local update not uploaded can accumulate over time, causing a delay. Such a delay can eventually deviate the iteration direction from the required descent direction of the current model parameters [9]. If this delay accumulates over multiple rounds, it can cause significant issues. When larger parameters always cover smaller parameters, sparsification can lead to a greater loss. Therefore, it is crucial to consider the impact of sparsification and ensure that smaller parameters are not neglected in the updating process. Another primary concern for FL systems is protecting user privacy. A series of studies [10; 11] have demonstrated that FL can leak sensitive information through the sharing of intermediate model updates. To address this issue, FL commonly integrates Differential Privacy (DP) [12], Homomorphic Encryption (HE) [13], and Secure Multiparty Computation (SMC) [14] for model training, which ensures that the transmitted model information remains confidential. HE enables aggregations to be performed on encrypted data [15; 16]; however, it is computationally intensive to execute computations in the encrypted domain. SMC can be used to securely aggregate local model updates without leaking them but it also suffers from the communication bottleneck typical of conventional distributed training. [PERSON] et al. (2017) proposed Secure Aggregation (SA) [17], which permits a server to calculate the sum of large data vectors held by mobile devices in a secure manner without disclosing each user's individual contribution. Nevertheless, implementing SA necessitates significant additional resources in terms of communication and computing to ensure privacy protection. The challenge of Federated Learning (FL) lies in building a protocol that ensures privacy protection and computational and communication efficiency, without significantly affecting accuracy. In this paper, we propose an efficient and secure FL framework based on gradient and mask sparsification, which comprises two components: time-varying hierarchical gradient sparsification and encryption mask sparsification. The time-varying hierarchical gradient sparsification algorithm balances the numerical size differences of the network parameters at different layers, reducing the loss caused by the sparsification process. Additionally, we sparsify the encryption mask in the secure aggregation framework, reducing the total amount of data sent, thereby improving communication efficiency and ensuring security. Our contributions can be summarized as follows:  
1. We propose an efficient and secure FL framework based on gradient and mask sparsification, which addresses the challenges of privacy protection and computational and communication efficiency in FL. 2. We introduce a time-varying hierarchical gradient sparsification algorithm that balances the numerical size differences of the network parameters at different layers, thereby reducing the loss caused by sparsification. Moreover, we propose to sparsify the encryption mask in the secure aggregation framework to reduce the total amount of data sent, improve communication efficiency, and ensure security. 3. Our experiments on the MNIST, Fashion-MNIST, and CIFAR-10 datasets prove that our method can reduce the upload communication costs to approximately 2.9% to 18.9% of the conventional FL algorithm when the sparsity rate is 0.01. The structure of this work is organized as follows. Section 2 provides an introduction to the related works and current scholarly advancements in gradient sparsification and secure aggregation. In Section 3, we present an efficient and secure federated learning framework that incorporates time-varying hierarchical gradient sparsification and encryption mask sparsification. Section 4 outlines the experimental settings and methodology, including the results. Finally, in Section 5, we present our conclusions regarding the proposed framework.