We present a rigorous model for secure reactive systems in asynchronous networks with a sound cryptographic semantics, supporting abstract specifications and the composition of secure systems. This enables modular proofs of security, which is essential in bridging the gap between the rigorous proof techniques of cryptography and toolsupported formal proof techniques. The model follows the general simulatability approach of modern cryptography. A variety of network structures and trust models

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... be described, such as static and adaptive adversaries; some examples of this are given. As an example of our specification methodology we provide an abstract and complete specification for Secure Message Transmission, improving on recent results by Lynch, and verify one concrete implementation. Our proof is based on a general theorem on the security of encryption in a reactive multi-user setting, generalizing a recent result by Bellare et.al.