The Open Science projects are also aimed at strongly encouraging the use of Cloud technologies and High Performance Computing (HPC), for the benefit of European researchers and universities. The emerging paradigm of Open Science enables an easier access to expert knowledge and material; however, it also raises some challenges regarding the protection of personal data, considering that part of the research data are personal data thus subjected to the EU’s General Data Protection Regulation (GDPR). This paper investigates the concept of scientific research in the field of data protection, with regard both to the European (GDPR) and national (Luxembourg Data Protection Law) legal framework for the compliance of the HPC technology. Therefore, it focuses on a case study, the HPC platform of the University of Luxembourg (ULHPC), to pinpoint the major data protection issues arising from the processing activities through HPC from the perspective of the HPC platform operators. Our study illustrates where the most problematic aspects of compliance lie. In this regard, possible solutions are also suggested, which mainly revolve around (1) standardisation of procedures; (2) cooperation at institutional level; (3) identification of guidelines for common challenges. This research is aimed to support legal researchers in the field of data protection, in order to help deepen the understanding of HPC technology’s challenges and universities and research centres holding an HPC platform for research purposes, which have to address the same issues.