Struik Security Consultancy This document specifies how to represent Montgomery curves and (twisted) Edwards curves as curves in short-Weierstrass form and illustrates how this can be used to carry out elliptic curve computations leveraging existing implementations and specifications of, e.g., ECDSA and ECDH using NIST prime curves. We also provide extensive background material that may be useful for implementers of elliptic curve cryptography.