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The TMN protocol is a secure key exchange protocol for mobile communication system. Its security has been analyzed thoroughly by many approaches, and many attacks have been found. Recently, we have developed a new Coloured Petri Net (CPN) approach to analyze cryptographic protocols, and then applied it to analyze the TMN protocol with the homomorphic property of the underlying public-key encryption. As preliminary analyses, we found two new attacks of the protocol. In this paper, we extend our previous works in two aspects. Firstly, we compare the performance between our new method and a traditional method to analyze attacks in cryptographic protocols. Surprisingly, our method is more efficient when the number of states and traces are large. Secondly, we found three new and interesting variants of our previous attacks.