In this paper we focus on building a large scale keyword search service over structured Peer-to-Peer (P2P) networks. Current state-of-the-art keyword search approaches for structured P2P systems are based on inverted list intersection. However, the biggest challenge in those approaches is that when the indices are distributed over peers, a simple query may cause a large amount of data to be transmitted over the network. We propose a new P2P keyword search scheme, called "Proof', to reduce network traffic for queries. The key idea is storing a content summary for each web page in the inverted list, so that a query can be processed by only transmitting a small size of candidate results. Our simulation results showed that, compared with previous DHT-based P2P systems, Proof can dramatically reduce network traffic and computation time. It provides 100% precision and 90.09% recall of search results, at an acceptable cost of storage overhead, even when the number of peers and documents increases continually.