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With the development of the peer-to-peer technology, a lot of lookup protocols have come out. Although we can benefit from different protocols separately, our research shows that given a proper model, most of the seemingly different protocols can be classified to a same framework. Since the essence of P2P lookup protocol is to find a specific node from network, some classic lookup arithmetic models can be naturally considered. In this paper, we firstly introduce the binary tree model to analyze some popular P2P lookup protocols, then give an improved Chord arithmetic based on the binary tree.