Abstract: Quantum no-cloning states that it is physically impossible to clone a quantum state. No-cloning is a central to the study of quantum cryptography, where it allows for objects such as physically unforgeable currency. In this work, I study two strong variants of no-cloning: (1) public key quantum money, where the would-be cloner is given a verification oracle for checking if it successfully cloned; and (2) quantum lightning, where the cloner even knows all the details of how the initial state was constructed. I then give a variety of results for public key quantum money and quantum lightning, yielding new constructions and interesting connections to other areas of cryptography.