Over the last years, visual localization and mapping solutions have been adopted by an increasing number of mixed reality and robotics systems. The recent trend towards cloud-based localization and mapping systems has raised significant privacy concerns. These are mainly grounded by the fact that these services require users to upload visual data to their servers, which can reveal potentially confidential information, even if only derived image features are uploaded. Recent research addresses some of these concerns for the task of image-based localization by concealing the geometry of the query images and database maps. The core idea of the approach is to lift 2D/3D feature points to random lines, while still providing sufficient constraints for camera pose estimation. In this paper, we further build upon this idea and propose solutions to the different core algorithms of an incremental Structure-from-Motion pipeline based on random line features. With this work, we make another fundamental step towards enabling privacy preserving cloud-based mapping solutions. Various experiments on challenging real-world datasets demonstrate the practicality of our approach achieving comparable results to standard Structure-from-Motion systems.