Many authentication and key exchange protocols are built using an accepted set of standard concepts such as Diffie-Hellman key exchange, nonces to avoid replay, certificates from an accepted authority, and encrypted or signed messages. We introduce a basic framework for deriving security protocols from such simple components. As a case study, we examine the structure of a family of key exchange protocols that includes Station-To-Station (STS), ISO-9798-3, Just Fast Keying (JFK), IKE and related protocols, deriving all members of the family from two basic protocols using a small set of re.nements and protocol transformations. As initial steps toward associating logical derivations with protocol derivations, we extend a previous security protocol logic with preconditions and temporal assertions. Using this logic, we prove the security properties of the standard signature based Challenge-Response protocol and the Diffie-Hellman key exchange protocol. The ISO-9798-3 protocol is then proved correct by composing the correctness proofs of these two simple protocols.