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Determining if two protocols can be securely run alongside each other requires analyzing the independence of the involved protocols. In this paper we construct a canonical model of security protocols that allows us to conduct a syntactical analysis on the independence of multiple security protocols. By integrating participant knowledge in the model, we are able to detect subtle multi-protocol attacks, where the types of certain message components can not be checked, also known as type-flaw attacks. Of special interest is the construction of messages in the proposed model, which is made by mapping each message component from the regular specification to a type. We provide a theorem for analyzing the independence of security protocols and illustrate its applicability by analyzing two protocols.