Many computer vision systems require users to upload image features to the cloud for processing and storage. Such features can be exploited to recover sensitive information about the scene or subjects, e.g., by reconstructing the appearance of the original image. To address this privacy concern, we propose a new privacy-preserving feature representation. The core idea of our work is to drop constraints from each feature descriptor by embedding it within an affine subspace containing the original feature as well as one or more adversarial feature samples. Feature matching on the privacy-preserving representation is enabled based on the notion of subspace-to-subspace distance. We experimentally demonstrate the effectiveness of our method and its high practical relevance for applications such as crowd-sourced 3D scene reconstruction and face authentication. Compared to the original features, our approach has only marginal impact on performance but makes it significantly more difficult for an adversary to recover private information.