Process mining aims to bridge the gap between data science and process science by providing a variety of powerful data-driven analyses techniques on the basis of event data. These techniques encompass automatically discovering process models, detecting and predicting bottlenecks, and finding process deviations. In process mining, event data containing the full breadth of resource information allows for performance analysis and discovering social networks. On the other hand, event data are often highly sensitive, and when the data contain private information, privacy issues arise. Surprisingly, there has currently been little research toward security methods and encryption techniques for process mining. Therefore, in this paper, using abstraction, we propose an approach that allows us to hide confidential information in a controlled manner while ensuring that the desired process mining results can still be obtained. We show how our approach can support confidentiality while discovering control-flow and social networks. A connector method is applied as a technique for storing associations between events securely. We evaluate our approach by applying it on real-life event logs.