The dramatic changes in telecommunications and computing technology as evidenced in the Internet and WWW have sparked a revolution in electronic commerce (e-commerce). In fact, many organisations are exploiting the opportunities of Internet-based e-commerce solutions, and many more are expected to follow. But in spite of the well-published success stories, many businesses and consumers are cautious about e-commerce, and security concerns are often cited as being the most important barrier. In this paper, we identify security and fairness in e-commerce transactions as basic requirements demanded by any participant in electronic markets. We discuss different phases of e-commerce transactions and study security requirements which are important to guarantee during each of the phases. In order to develop trust for e-commerce transactions we propose 1. COPS, a technical infrastructure for building adaptable electronic markets with main focus on security and fairness, and 2. MOSS, a business process reengineering methodology for analysing and modelling the security semantics of business transactions in order to transfer them to electronic markets. Both, COPS and MOSS are helpful to control the risks involved in dealing (trading) with untrusted parties in an open e-commerce environment.