arXiv:2410.02544v3 Announce Type: replace Abstract: As one of the most well-studied cohesive subgraph models, the $k$-core is widely used to find graph nodes that are ``central'' or ``important'' in many applications, such as biological networks, social networks, ecological networks, and financial networks. For Decentralized Online Social Networks (DOSNs), where each vertex is a client as a single computing unit, distributed k-core decomposition algorithms have already been proposed. However, current distributed approaches fail to adequately protect privacy and security. In today's data-driven world, data privacy and security have attracted more and more attention, e.g., DOSNs are proposed to protect privacy by storing user information locally without using a single centralized server. In this work, we are the first to propose the secure version of the distributed $k$-core decomposition.