The use of reputation systems has been proposed for various applications, e. g., to estimate the trustworthiness of sellers and buyers in electronic transactions. Reputation systems collect opinions of users about properties of certain services, subjects and other users and evaluate these opinions. It is important that the results of reputation systems are consistent with intuitive expectations of its users, which highly depends on the properties of the underlying trust model. The trust model defines the representation of the trust values as well as the computation of trust values for derived trust relations. We propose a new sophisticated computational model of trust which seamlessly integrates authentication verification into the trust evaluation process and which is suitable especially for open, decentralized reputation systems. It consists of definitions of trust and authentication relations, inference rules and three downward compatible trust calculi. It is therefore possible to represent and evaluate trust values with different levels of detail. The model reflects all relevant aspects and properties of trust and authentication relations and therefore avoids any counterintuitive effects.