## 1 Introduction  
With the rapid development of the Internet of Things (IoT) and edge computing, an increasing number of devices are being deployed, leading to the generation of vast amounts of data. These data, often generated in sensitive environments such as healthcare, smart homes, and industrial systems, demand high communication efficiency and strong privacy protection mechanisms [1]. Ensuring data privacy while maintaining system efficiency has become a critical challenge in IoT environments, where numerous devices are interconnected and generate continuous streams of information [2]. However, IoT devices are highly heterogeneous, exhibiting significant differences in computational capabilities, memory resources, and network connectivity. This heterogeneity poses substantial challenges for data privacy and efficient communication [3, 4, 5]. Devices with limited resources may struggle to participate effectively in a distributed system, resulting in imbalanced workloads, latency, and reduced system robustness [6]. The diversity of device capabilities and network conditions makes it difficult to design a one-size-fits-all solution for privacy-preserving data processing and communication efficiency. Federated learning (FL), as exemplified by algorithms such as FedAvg, enables decentralized training by coordinating multiple devices to collaboratively learn a shared global model without exchanging raw data [7]. The FL process typically consists of several iterative communication rounds, where each round involves three main steps: **(1) initialization**, where the server sends the global model to selected devices; **(2) local training**, where devices train the model using their local data; and **(3) aggregation**, where devices upload their model updates, and the server combines these updates to refine the global model. Despite its potential, traditional FL approaches face several limitations in heterogeneous IoT environments. A key challenge is the high round time that represents the total time for completing an iteration of the FL process. A round time is composed of three parts, including the server distributing the global model to selected devices, the local training performed on each device, and the subsequent uploading of locally updated models back to the server for aggregation. In heterogeneous IoT settings, slower devices (or stragglers) can significantly prolong the round time, therefore delaying convergence [8]. This delay not only affects overall efficiency but also increases energy consumption and resource usage for resource-constrained devices. Furthermore, the computational and communication overhead imposed by centralized FL methods remains burdensome, limiting their practicality in such environments [9]. To this end, hierarchical federated learning (HFL) frameworks have emerged as a promising approach to address these challenges [10; 11], such as HierFAVG [12]. By introducing intermediate aggregation layers (e.g., edge servers), compared to FedAvg, HFL reduces communication overhead to the central cloud and enables localized aggregation, therefore improving scalability and resource utilization. Nevertheless, most existing HFL solutions focus on architectural optimization and ignore critical aspects such as security mechanisms, device heterogeneity, and asynchronous coordination [13]. These limitations leave gaps in ensuring both privacy and efficiency under highly dynamic and heterogeneous IoT conditions. Strengthening the privacy mechanisms employed in FL has led to the proposal of several advanced techniques, such as homomorphic encryption, secure multi-party computation (SMPC), and differential privacy have been proposed [14; 15; 16]. Although these methods provide strong security guarantees, they impose significant computational and storage requirements, making them impractical for IoT devices [17; 18].