Data minimization has become a paradigm to address privacy concerns when collecting and storing personal data. In this paper we present two new approaches, RSTxFM and RRTxFM, to estimate the cardinality of a dataset while ensuring differential privacy. We argue that privacy-preserving cardinality estimators are able to realize strong privacy requirements. Both approaches are based on a probabilistic counting algorithm which has a logarithmic space complexity. We combine this with a randomization technique to provide differential privacy. In our analysis, we detail the privacy and utility guarantees and expose the impact of the various parameters. Moreover, we discuss workforce analytics as application area where strong privacy is paramount.