Authentication and copyright identification are two critical security issues for medical images. Although zerowatermarking schemes can provide durable, reliable and distortion-free protection for medical images, the existing zerowatermarking schemes for medical images still face two problems. On one hand, they rarely considered the distinguishability for medical images, which is critical because different medical images are sometimes similar to each other. On the other hand, their robustness against geometric attacks, such as cropping, rotation and flipping, is insufficient. In this study, a novel discriminative and robust zero-watermarking (DRZW) is proposed to address these two problems. In DRZW, content-based features of medical images are first extracted based on completed local binary pattern (CLBP) operator to ensure the distinguishability and robustness, especially against geometric attacks. Then, master shares and ownership shares are generated from the content-based features and watermark according to (2,2) visual cryptography. Finally, the ownership shares are stored for authentication and copyright identification. For queried medical images, their content-based features are extracted and master shares are generated. Their watermarks for authentication and copyright identification are recovered by stacking the generated master shares and stored ownership shares. 200 different medical images of 5 types are collected as the testing data and our experimental results demonstrate that DRZW ensures both the accuracy and reliability of authentication and copyright identification. When fixing the false positive rate to 1.00%, the average value of false negative rates by using DRZW is only 1.75% under 20 common attacks with different parameters.