## 2 Related Work  
In contrast to traditional centralized machine learning techniques, for which all local datasets are uploaded to one server, the technique we study is known as federated learning or collaborative learning. In federated learning, the primary objective is to develop a method that enables parties to jointly compute the parameters of a machine learning model based on their input data while protecting the privacy of their individual data. To meet the security requirement, trusted servers can be used to protect the confidentiality of data and perform computations efficiently. The security of many known secure computation schemes for linear regression requires servers [10; 11; 12; 13; 14; 15]. Some of the schemes use only one server [10; 11; 13]. Some of the schemes use two servers: one for cryptography service and the other for computation [12; 14; 15]. There are also different ways to use multiple servers. For example, in [PERSON] et al. 's scheme [11], a trusted server is only needed in the pre-distribution phase to do initialization. On the other hand, in [PERSON] et al. 's [10] and [PERSON] et al. 's schemes [13], the server is required to do computational tasks, but the server is only required to be semi-honest. Federated learning can also be considered as secure multiparty computation or privacy-preserving computation. Secure multiparty computation has been widely studied by many cryptographers [16; 17; 18]. Recently, [PERSON] et al. developed algorithms under secure multiparty computation that enable pharmaceutical institutions to achieve high-quality models to advance drug discovery without revealing private drug-related information [19]. The security of most existing secure multiparty computations depends on computationally hard problems, such as factoring large integers or solving discrete logarithms in a large group. Some of the schemes are based on [PERSON]'s garble circuit combined with secure computation for computing inner products [12]. Some of the schemes are based on homomorphic encryption to ensure the security of the data [14]. [PERSON] et al. proposed a scheme that does not require trusted servers [20], but it need [PERSON]'s cryptosystem, which is a public-key homomorphic cryptosystem. Recently, [PERSON] et al. proposed two noninteractive federated learning schemes with privacy-preserving for loMT [21], but they need trusted authority and [PERSON]'s cryptosystem. These cryptosystems, including [PERSON]'s garbled circuits, are usually computationally intensive. Our proposed linear regression scheme operates without encryption, allowing us to circumvent the above issues and achieve efficient implementation. Some of the known schemes do not use the closed form of the optimum solution for linear regression [12; 13]. While the authors claim that the advantage is that their scheme does not require computing the matrix inverse, the disadvantage is that the result is only an approximation. On top of that, this computational method has to send gradient descent or other relevant data multiple times to make the model parameters accurate enough. It has been shown that sending gradient descent data iteratively can reveal enough information for the attacker to infer the values of the training data [22; 23]. For each dataset, our scheme only sends the aggregated data once, and we show that the information leaked is too small for any unauthorized party to infer information about the other party's data. Note that this technique works well for linear regression problems. Other federated learning problems may not be able to avoid iterative sending of gradient descent data and may require other techniques to preserve privacy. For example, when using Deep Neural Networks (DNNs), [PERSON] et al. proposed a double-masking protocol to guarantee the confidentiality of users' local gradients during federated learning [24]. Finally, we perform a comparative analysis of various federated learning schemes designed for linear regression.