Mining complex data is an essential and at the same time challenging task. Therefore, organizations pass on their encrypted data to service providers carrying out such analyses. Thus, encryption must preserve the mining results. Many mining algorithms are distance-based. Thus, we investigate how to preserve the results for such algorithms upon encryption. To this end, we propose the notion of distance-preserving encryption (DPE). This notion has just the right strictness - we show that we cannot relax it, using formal arguments as well as experiments. Designing a DPE scheme is challenging, as it depends both on the data set and the specific distance measure in use. We propose a procedure to engineer DPE-schemes, dubbed DisPE. In a case study, we instantiate DisPE for SQL query logs, a type of data containing valuable information about user interests. In this study, we design DPE schemes for all SQL query distance measures from the scientific literature. We formally show that one can use a combination of existing secure property-preserving encryption schemes to this end. Finally, we discuss on the generalizability of our findings using two other data sets as examples.