Abstract. Simulation-based security notions for cryptographic protocols are regarded as highly desirable, primarily because they admit strong composability and, consequently, a modular design. In this paper, we give a simulation-based security definition for two-round authenticated message exchange and show that a concrete protocol, 2AMEX-1, satisfies our security property, that is, we provide an ideal functionality for tworound authenticated message exchange and show that 2AMEX-1 realizes it securely. To model the involved public-key infrastructure adequately, we use a joint-state approach.