In this paper, a cryptographic protocol together with its cryptographic algorithms is regarded as one system, and a security model for the system is built. Based on assume-guarantee compositional reasoning techniques, a new assume-guarantee based reasoning rule and algorithm are proposed, and the soundness of the rule is proved. In realizing model checking to the cryptographic protocol system, several difficulties are solved chiefly such as decomposition of the system, generation of assumed functions, and specifying security properties in forms of both logic formulas and processes. Using this security model and assume-guarantee based reasoning techniques, the kerberos cryptographic protocol system is verified.