The paper develops a foundation for reasoning about protocol security. We adopt a model-based approach for defining protocol security properties. This allows us to describe security properties in greater detail and precision than previous frameworks. Our model allows us to reason about the security of protocols, and considers issues of beliefs of agents, time, and secrecy. We prove a composition theorem which allows us to state sufficient conditions on two secure protocols A and B such that they may be combined to form a new secure protocol C. Moreover, we give counter-examples to show that when the conditions are not met, the protocol C may not be secure.