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Cryptographic protocols have been widely used to protect communications over insecure network environments. Existing cryptographic protocols usually contain flaws. To analyze these protocols and find potential flaws in them, the secure properties of them need be studied in depth. This paper attempts to provide a new framework to analyze and prove the secure properties in these protocols. A number of predicates and action functions are used to model the network communication environment. Domain rules are given to describe the transitions of principals' knowledge and belief states. An example of public key authentication protocols has been studied and analysed.