The ease of digital data dissemination has spurred an amplified interest in technologies related to data privacy and right protection. We examine how both goals can be achieved simultaneously by constructing modified data instances that are both differentially private and right protected. The proposed method first produces a sketch of the dataset via random projection and then perturbs the sketch just enough to ensure privacy. The right-protection mechanism inserts small noise in the dataset which subsequently can be used to verify ownership. We provide analytical privacy, right-protection, and utility guarantees. Our utility guarantees ensure approximate preservation of pairwise distances, thus mining operations such as search, classification, and clustering can be performed on the differentially private and right protected dataset.