The current work deals with the problem of resource management in P2P networks. The topological properties of the overlay network are critical factors that dominate the performance of P2P networks. The inverse Kautz digraph is a good topology to construct the overlay network. We discuss an efficient DHT-based overlay network (MREIK) with Byzantine fault tolerance. MREIK based on many rings which embeds inverse Kautz digraphs, to enable multi-path P2P routing. Each node maintains a maximum limited number of 2d + 3 entries in its routing table, and any resource is distributed at an exit node based on the longest prefix matching rule. It supports both exact and similarity resources search efficiently. MREIK reduces REIK with one ring maintenance cast and provides high quality routing service.