This research focuses on introducing a novel concept to design a scalable, hierarchical interest-based overlay Peer-to-Peer (P2P) system. We have used Linear Diophantine Equation (LDE) as the mathematical base to realize the architecture. Note that all existing structured approaches use Distributed Hash Tables (DHT) and Secure Hash Algorithm (SHA) to realize their architectures. Use of LDE in designing P2P architecture is a completely new idea; it does not exist in the literature to the best of our knowledge. We have shown how the proposed LDE-based architecture outperforms some of the most well established existing architecture. We have proposed multiple effective data query algorithms considering different circumstances, and their time complexities are bounded by (2+ r/2) only; r is the number of distinct resources. Our alternative lookup scheme needs only constant number of overlay hops and constant number of message exchanges that can outperform DHT-based P2P systems. Moreover, in our architecture, peers are able to possess multiple distinct resources. A convincing solution to handle the problem of churn has been offered. We have shown that our presented approach performs lookup queries efficiently and consistently even in presence of churn. In addition, we have shown that our design is resilient to fault tolerance in the event of peers crashing and leaving. Furthermore, we have proposed two algorithms to response to one of the principal requests of P2P applications’ users, which is to preserve the anonymity and security of the resource requester and the responder while providing the same light-weighted data lookup.