Advances in DNA sequencing create new opportunities for the use of DNA data in healthcare for diagnostic and treatment purposes, but also in many other health and well-being services. This brings new challenges with regard to the protection and use of this sensitive data. Thus, special technical means of protection should safeguard critical DNA data and create trust for patients and consumers of lifestyle services. In particular an interesting research challenge is to design secure operations on DNA sequences in the encrypted domain that allow a person to engage into a DNA-based service and obtain required (medical) answers without revealing his/her DNA. We focus in this paper on this topic and present a solution to a particular problem of privacy-preserving matching of DNA sequences which can be used in clinical trials or other DNA services.