## 1 Introduction  
The rapid increase in the amount of digital healthcare information in the form of EHRs, wearables, telemedicine, and others has brought vast potential for the enhancement of patient care and the development of new knowledge in medicine. However, there is always the problem of protecting the privacy of the patients and their records. Centralizedapproaches common in machine learning where raw data is fed to a centralized server are extremely vulnerable to data breaches. Federated learning (FL) has evolved as a decentralized learning model in which a set of institutions can train a model together without directly sharing raw data. However, the application of FL in the healthcare sector, such as in the US where it is governed by HIPAA and in the EU where it is regulated by GDPR, calls for secure privacy preservation measures that address FL's privacy and model accuracy concerns. Previous work has discussed the rapid increase in the amount of digital healthcare data due to the use of EHRs, wearables, and telemedicine [1; 2]. While all of this represents a wealth of new information that might improve care and advance the field of medicine, it raises fresh concerns about patient privacy and confidentiality. Centralized ML techniques where raw data is sent to the central server are not safe and are privacy invasive by design. This is particularly so in the area of health where there are strict legal requirements on how personal and health information should be processed. Federated learning (FL) provides a way for institutions to collaboratively train the models without passing the raw data, thus reducing the risk of data leakage [3]. The advancement shows that the FL is not devoid of shortcomings. The issues like scalability, data security, and the integration of data from various sources across multiple institutions remain relevant [4]. For applying FL in sectors such as healthcare which are governed by tight legal policies like HIPAA and GDPR, privacy-preserving measures need enhancement. DP is one such approach used to protect privacy during model training, but it reduces model accuracy and efficiency [5]. Thus, there is an urgent need for developing new strategies which can ensure good privacy while preserving high model utility, especially in such fields as healthcare. The opportunity for enhancing patients' care and enhancing medical research based on the constantly increasing and exponentially growing volume of stored and processed digital healthcare data drawn from EHRs, wearable devices, and telemedicine is enormous [1]. However, this data is full of highly sensitive patient information and its protection must be stringent, especially when dealing with regulatory standards such as HIPAA and GDPR. Centralized machine learning, where raw data is transmitted to a central server, poses risks of hacking and privacy losses. There are risks associated with federated learning (FL) approach which are avoided through training models across institutions and without raw data [2]. However, FL has challenges, some of which include scalability, data heterogeneity, and data privacy, especially in healthcare context [3]. The proposed methodology outlines the Hierarchical Federated Learning (HFL) structure with a two-level aggregation structure. In the first tier, local models are trained in healthcare institutions (like hospitals); here, the patient data remain local, and noise is added using Local Differential Privacy. These noisy local model updates are transmitted to the relevant regional centers where the individual updates are not exposed by employing Secure Multi-Party Computation. These updates are then accumulated at the regional level and transmitted to a global server where Global Differential Privacy is performed to obtain the overall model. Furthermore, Homomorphic Encryption is used to protect the updates of models during the computation. However, privacy-preserving techniques like DP and SMPC may reduce the model's accuracy and increase computational expenses.