The field of medical imaging AI is currently undergoing rapid transformations, with methodical research increasingly translated into clinical practice. Despite these successes, research suffers from knowledge silos, hindering collaboration and progress: Existing knowledge is scattered across publications and many details remain unpublished, while privacy regulations restrict data sharing. In the spirit of democratizing of AI, we propose a framework for secure knowledge transfer in the field of medical image analysis. The key to our approach is dataset "fingerprints", structured representations of feature distributions, that enable quantification of task similarity. We tested our approach across 71 distinct tasks and 12 medical imaging modalities by transferring neural architectures, pretraining, augmentation policies, and multi-task learning. According to comprehensive analyses, our method outperforms traditional methods for identifying relevant knowledge and facilitates collaborative model training. Our framework fosters the democratization of AI in medical imaging and could become a valuable tool for promoting faster scientific advancement.