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Secure communication generally begins with a~connection establishment phase in which messages are exchanged by client and server protocol software to generate, share, and use secret data or keys. This message exchange is referred to as an authentication or key distribution cryptographic protocol. CAPSL is a formal language for specifying cryptographic protocols. It is also useful for addressing the correctness of the protocols on an abstract level, rather than the strength of the underlying cryptographic algorithms. We outline the design principles of CAPSL and its integrated specification and analysis environment. Protocols for secure group management are essential in applications that are concerned with confidential authenticated communication among coalition members, authenticated group decisions, or the secure administration of group membership and access control. We will also discuss our progress on designing a new extension of CAPSL for multicast protocols, called MuCAPSL.